15_purification_sampling.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Sampling of Purification MPS\n",
    "This notebook demonstrates how to sample basis states from a purification MPS to evaluate expectation values. While we demonstrate this for magnetization, a sum of local quantities $\\langle Z_i \\rangle$, sampling could be useful to stochastically evaluate non-local expectation values where contraction of the tensor network for exact evaluation is expensive. To demonstrate this functionality, we find the purification of the thermal density matrix $\\rho \\propto e^{-\\beta H}$ for the transverse field Ising model as a function of inverse temperature $\\beta$. We represent the density matrix as a purified pure state $|\\psi \\rangle$ on an enlarged Hilbert space $\\mathcal{H}_p \\otimes \\mathcal{H}_a $ such that $\\rho = \\mathrm{Tr}_a |\\psi \\rangle \\langle \\psi |$.\n",
    "\n",
    "The algorithm from sampling purification MPS is a simple extension of that for sampling MPS, explained in detail in the following two papers:\n",
    "1. https://arxiv.org/abs/1002.1305\n",
    "2. https://arxiv.org/abs/1201.3974"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1676db25-ef96-4ce2-aeae-6f0b6e937cd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "from time import time\n",
    "import logging\n",
    "logging.basicConfig(level=logging.INFO)\n",
    "\n",
    "import tenpy\n",
    "from tenpy.models.tf_ising import TFIChain\n",
    "from tenpy.networks.purification_mps import PurificationMPS\n",
    "from tenpy.algorithms.purification import PurificationTEBD, PurificationApplyMPO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "296dfee9-7b27-49be-81fc-23c540f8df93",
   "metadata": {},
   "source": [
    "Run purification TEBD and measure magnetization on each site, both by contracting the tensor network (really by using orthogonality conditions to avoid most of the work) or sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "58a7e566-a94f-4b91-8f97-3f3cb4f25d2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def imag_tebd(L=30, beta_max=3., dt=0.05, order=2, bc=\"finite\", num_samples=1000, chi_max=100, sample_all=True):\n",
    "    model_params = dict(L=L, J=1., g=1.2)\n",
    "    M = TFIChain(model_params)\n",
    "    psi = PurificationMPS.from_infiniteT(M.lat.mps_sites(), bc=bc)\n",
    "    options = {\n",
    "        'trunc_params': {\n",
    "            'chi_max': chi_max,\n",
    "            'svd_min': 1.e-8\n",
    "        },\n",
    "        'order': order,\n",
    "        'dt': dt,\n",
    "        'N_steps': 1\n",
    "    }\n",
    "    beta = 0.\n",
    "    eng = PurificationTEBD(psi, M, options)\n",
    "    Szs = [psi.expectation_value(\"Sz\")]\n",
    "    Szs_sample_sq, Szs_sample_nsq, sampling_time_sq, sampling_time_nsq = [], [], [], []\n",
    "    if sample_all:\n",
    "        sample_data = sample_purification(psi, num_samples)\n",
    "        Szs_sample_sq.append(sample_data[0][0])\n",
    "        Szs_sample_nsq.append(sample_data[1][0])\n",
    "        sampling_time_sq.append(sample_data[0][2])\n",
    "        sampling_time_nsq.append(sample_data[1][2])\n",
    "    betas = [0.]\n",
    "    psis = [psi.copy()]\n",
    "    while beta < beta_max:\n",
    "        beta += 2. * dt  # factor of 2:  |psi> ~= exp^{- dt H}, but rho = |psi><psi|\n",
    "        betas.append(beta)\n",
    "        eng.run_imaginary(dt)  # cool down by dt\n",
    "        Szs.append(psi.expectation_value(\"Sz\"))  # and further measurements...\n",
    "        if sample_all or np.isclose(beta, beta_max):\n",
    "            print(psi.chi)\n",
    "            sample_data = sample_purification(psi, num_samples)\n",
    "            Szs_sample_sq.append(sample_data[0][0])\n",
    "            Szs_sample_nsq.append(sample_data[1][0])\n",
    "            sampling_time_sq.append(sample_data[0][2])\n",
    "            sampling_time_nsq.append(sample_data[1][2])\n",
    "        psis.append(psi.copy())\n",
    "    return {'beta': betas, 'Sz': Szs, 'Sz_sample_sq': Szs_sample_sq, 'Sz_sample_nsq': Szs_sample_nsq, \n",
    "            'time_sq': sampling_time_sq, 'time_nsq': sampling_time_nsq, \n",
    "            'psi': psis}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edf84aca-e1c6-4467-bd66-588ab5883724",
   "metadata": {},
   "source": [
    "Below we repeatedly sample a purification MPS to determine the magnetization. Depending on the value of `sample_q`, we either sample the ancilla leg (`True`) or contract over it (`False`). The first is cheaper than the latter, with a cost of $\\mathcal{}(\\chi^2)$ compared to $\\mathcal{}(\\chi^3)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d3a7e9b7-c327-4791-a56c-0620bddd0786",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_purification(psi, num_samples):\n",
    "    data = []\n",
    "    for sample_q in [True, False]:\n",
    "        magnetization = []\n",
    "        start_time = time()\n",
    "        for i in range(num_samples):\n",
    "            sigmas, total_prob = psi.sample_measurements(sample_q, complex_amplitude=False)\n",
    "            magnetization.append(np.array(sigmas) - 1/2) # 1 index corresponds to spin up I guess\n",
    "        sample_time = time() - start_time\n",
    "        magnetization = np.row_stack(magnetization)\n",
    "        data.append((magnetization.mean(axis=0), magnetization, sample_time / num_samples))\n",
    "    return data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "034debc5",
   "metadata": {},
   "source": [
    "## Average magnetization as a function of $\\beta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e52aaab4-e840-45dc-a4f7-ac9c678eff0a",
   "metadata": {
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
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    {
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
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    {
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
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     "output_type": "stream",
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
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     "output_type": "stream",
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jakobunfried/tenpy/development/tenpy/tools/params.py:232: UserWarning: unused options for config PurificationTEBD:\n",
      "['N_steps', 'order']\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
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    {
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      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
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    {
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    {
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      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
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      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# note: this cell is skipped in pytest\n",
    "data_tebd = imag_tebd(L=30, beta_max=3.0, num_samples=50)\n",
    "\n",
    "plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz'], axis=1), label='TEBD')\n",
    "plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz_sample_sq'], axis=1), '.', label='TEBD; sampling q')\n",
    "plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz_sample_nsq'], axis=1), '.', label='TEBD; tracing q')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\beta$')\n",
    "plt.ylabel(r'total $S^z$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bca56ba-85f3-4960-9ea8-60f7a32888d1",
   "metadata": {},
   "source": [
    "Do a quick sanity check, if the above curves actually agree.\n",
    "Use smaller $L$ and $\\beta$, such that we can use this as part of the github actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "02838f00-fa8a-4373-8900-b648cb9a9158",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=20\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2486712411, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4807745902, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6842967410, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8538132645, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9896631609, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0957122376, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1772055723, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2393667416, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2867281260, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3229382086, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3508091638, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n",
      "0.12407017068350712\n",
      "0.10186772056872069\n"
     ]
    }
   ],
   "source": [
    "data = imag_tebd(L=20, beta_max=1.0, num_samples=50)\n",
    "\n",
    "diffs_sampling = np.sum(data['Sz'], axis=1) - np.sum(data['Sz_sample_sq'], axis=1)\n",
    "mse_sampling = np.sum(np.abs(diffs_sampling) ** 2 ) / len(diffs_sampling)\n",
    "diffs_tracing = np.sum(data['Sz'], axis=1) - np.sum(data['Sz_sample_nsq'], axis=1)\n",
    "mse_tracing = np.sum(np.abs(diffs_tracing) ** 2 ) / len(diffs_tracing)\n",
    "print(mse_sampling)\n",
    "print(mse_tracing)\n",
    "assert mse_sampling < 1\n",
    "assert mse_tracing < 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e0b9369-ab52-46ab-a784-4cc611721aea",
   "metadata": {},
   "source": [
    "Now we look at sampling time as a function of $\\beta$. We expect this to be independent of $\\beta$ and only dependent on $\\chi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e438e48c-593b-4d22-bca7-b921a713bdd0",
   "metadata": {
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jakobunfried/tenpy/development/tenpy/tools/params.py:232: UserWarning: unused options for config PurificationTEBD:\n",
      "['N_steps', 'order']\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data_tebd['beta'], data_tebd['time_sq'], '.', label='TEBD; sampling q')\n",
    "plt.plot(data_tebd['beta'], data_tebd['time_nsq'], '.', label='TEBD; tracing q')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\beta$')\n",
    "plt.ylabel(r'Sampling Time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35821e01-ef39-48bf-86b5-876d8feaa53a",
   "metadata": {},
   "source": [
    "## Sampling time dependence on chi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6cc1da7d-8e0a-4c9f-947a-b13a3c0e3ced",
   "metadata": {
    "scrolled": true,
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=2\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460704684, max(S)=0.0172499542\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756295855, max(S)=0.0532187236\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6766525889, max(S)=0.0966746449\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8436355045, max(S)=0.1410008935\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9768282106, max(S)=0.1823408159\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0800497086, max(S)=0.2189349620\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1585539424, max(S)=0.2503366410\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2176145022, max(S)=0.2768028450\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2618331065, max(S)=0.2988946378\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.2949295484, max(S)=0.3172523022\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3197791128, max(S)=0.3324856739\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3385459894, max(S)=0.3451301838\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3528341236, max(S)=0.3556364310\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3638222698, max(S)=0.3643749599\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3723733559, max(S)=0.3716467144\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.3791185376, max(S)=0.3776946110\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.3845199431, max(S)=0.3827142764\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.3889167423, max(S)=0.3868632701\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.3925586707, max(S)=0.3902687015\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.3956303182, max(S)=0.3930333886\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.3982687029, max(S)=0.3952407804\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4005759943, max(S)=0.3969588716\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4026287395, max(S)=0.3982433085\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4044845733, max(S)=0.3991398545\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4061871111, max(S)=0.3996863519\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4077695311, max(S)=0.3999142853\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4092572046, max(S)=0.3998500337\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4106696360, max(S)=0.3995158765\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4120218982, max(S)=0.3989308037\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4133256987, max(S)=0.3981111736\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=4\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494809, max(S)=0.0532230133\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971354, max(S)=0.0967049716\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540073, max(S)=0.1411322267\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781012074, max(S)=0.1827166245\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825185679, max(S)=0.2197684742\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626408176, max(S)=0.2518954752\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236654898, max(S)=0.2793871022\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2700919103, max(S)=0.3028153664\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055347414, max(S)=0.3228138181\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3327751177, max(S)=0.3399727867\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3538999884, max(S)=0.3548001033\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3704540845, max(S)=0.3677145909\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3835735866, max(S)=0.3790538537\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3940930523, max(S)=0.3890868855\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4026267814, max(S)=0.3980270661\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4096290161, max(S)=0.4060437379\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4154377814, max(S)=0.4132718286\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4203065474, max(S)=0.4198195522\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4244270136, max(S)=0.4257744365\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4279455007, max(S)=0.4312079787\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4309747678, max(S)=0.4361792156\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4336025622, max(S)=0.4407374495\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4358978383, max(S)=0.4449243276\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4379153060, max(S)=0.4487754294\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4396987828, max(S)=0.4523214816\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4412836798, max(S)=0.4555892900\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4426988619, max(S)=0.4586024594\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4439680509, max(S)=0.4613819516\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4451108922, max(S)=0.4639465212\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=8\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014308, max(S)=0.1827168024\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193810, max(S)=0.2197692330\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430248, max(S)=0.2518978586\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236703781, max(S)=0.2793931551\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012469, max(S)=0.3028285287\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507023, max(S)=0.3228392682\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328001762, max(S)=0.3400176995\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539367912, max(S)=0.3548738039\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705053320, max(S)=0.3678285994\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836419271, max(S)=0.3792218274\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941809928, max(S)=0.3893244680\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027366149, max(S)=0.3983516592\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097627652, max(S)=0.4064742140\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155971581, max(S)=0.4138282015\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204929266, max(S)=0.4205226238\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246414203, max(S)=0.4266454364\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281886096, max(S)=0.4322682107\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312469127, max(S)=0.4374497211\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339037547, max(S)=0.4422386982\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362277928, max(S)=0.4466759411\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382734699, max(S)=0.4507959412\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400843695, max(S)=0.4546281348\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4416957037, max(S)=0.4581978748\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431361732, max(S)=0.4615271866\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444293699, max(S)=0.4646353619\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4455948410, max(S)=0.4675394269\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=12\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370349, max(S)=0.3548744860\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056887, max(S)=0.3678296982\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424292, max(S)=0.3792235047\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816790, max(S)=0.3893269208\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375311, max(S)=0.3983551228\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639652, max(S)=0.4064789662\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987036, max(S)=0.4138345672\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948869, max(S)=0.4205309799\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438716, max(S)=0.4266562160\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916334, max(S)=0.4322819071\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312505947, max(S)=0.4374668917\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339081830, max(S)=0.4422599668\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362330562, max(S)=0.4467019998\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382796566, max(S)=0.4508275513\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400915653, max(S)=0.4546661269\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417039908, max(S)=0.4582431474\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431456291, max(S)=0.4615807051\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444400661, max(S)=0.4646981557\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456068426, max(S)=0.4676125866\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=16\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639704, max(S)=0.4064789716\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987118, max(S)=0.4138345769\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948990, max(S)=0.4205309967\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438886, max(S)=0.4266562441\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916564, max(S)=0.4322819527\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506251, max(S)=0.4374669632\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082222, max(S)=0.4422600755\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331058, max(S)=0.4467021603\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797183, max(S)=0.4508277821\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916410, max(S)=0.4546664509\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040823, max(S)=0.4582435927\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457386, max(S)=0.4615813050\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444401956, max(S)=0.4646989497\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456069943, max(S)=0.4676136203\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=20\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506259, max(S)=0.4374669712\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331073, max(S)=0.4467021777\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797203, max(S)=0.4508278065\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916435, max(S)=0.4546664842\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040854, max(S)=0.4582436371\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457423, max(S)=0.4615813631\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402001, max(S)=0.4646990244\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456069997, max(S)=0.4676137150\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=24\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n",
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 16, 4]\n"
     ]
    }
   ],
   "source": [
    "datas_tebd = {}\n",
    "for chi in [2, 4, 8, 12, 16, 20, 24]:\n",
    "    datas_tebd[chi] = imag_tebd(L=30, beta_max=3.0, num_samples=50, chi_max=chi, sample_all=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7b9512eb-bd05-45cf-900b-a858e6669302",
   "metadata": {
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys([2, 4, 8, 12, 16, 20, 24])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datas_tebd.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c25cab64-2c33-4279-ada7-3532ec9f37ae",
   "metadata": {
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chis = list(datas_tebd.keys())\n",
    "plt.plot(chis, [datas_tebd[c]['time_sq'] for c in chis], '.', label='TEBD; sampling q')\n",
    "plt.plot(chis, [datas_tebd[c]['time_nsq'] for c in chis], '.', label='TEBD; tracing q')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\chi$')\n",
    "plt.ylabel(r'Sampling Time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26cfa69d-5870-4e8c-a0e9-46947d0bc8e0",
   "metadata": {},
   "source": [
    "At these small bond dimensions, $\\chi \\leq 24$, we do not see the expect scaling of sampling time with bond dimension. The transverse field Ising model is not complicated enough to generate large bond dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cba3532-a70e-4ba8-be48-c2242534a449",
   "metadata": {},
   "source": [
    "## Accuracy with increasing number of samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ebef5e-b6b1-4ae7-a12e-3145f5142fbc",
   "metadata": {},
   "source": [
    "Finally, we demonstrate that the error in expectation values from sampling decreases with the number of samples, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b971febf-13f9-454b-8e48-e64da7e6fc64",
   "metadata": {
    "scrolled": true,
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "/Users/jakobunfried/tenpy/development/tenpy/tools/params.py:232: UserWarning: unused options for config PurificationTEBD:\n",
      "['N_steps', 'order']\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.tools.params:TFIChain: reading 'L'=30\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0\n",
      "INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2\n",
      "INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')\n",
      "INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05\n",
      "INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100\n",
      "INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08\n",
      "INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "data_dict = {}\n",
    "for ns in [10, 25, 50, 100, 250, 500]:\n",
    "    data_tebd = imag_tebd(L=30, beta_max=3.0, num_samples=ns)\n",
    "    data_dict[ns] = data_tebd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cd3406ee-1888-4702-aa39-261a3c50f707",
   "metadata": {
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# note: this cell is skipped in pytest\n",
    "for ns in [10, 25, 50, 100, 250, 500]:\n",
    "    plt.plot(data_dict[ns]['beta'], np.sum(data_dict[ns]['Sz'], axis=1), label='TEBD')\n",
    "    plt.plot(data_dict[ns]['beta'], np.sum(data_dict[ns]['Sz_sample_sq'], axis=1), '.', label='TEBD; sampling q')\n",
    "    plt.plot(data_dict[ns]['beta'], np.sum(data_dict[ns]['Sz_sample_nsq'], axis=1), '.', label='TEBD; tracing q')\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.xlabel(r'$\\beta$')\n",
    "    plt.ylabel(r'total $S^z$')\n",
    "    plt.title(f\"Number of samples: {ns}\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4f714445-6b2a-4239-b92d-9e76bce9fafa",
   "metadata": {
    "tags": [
     "skip-execution"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([10, 25, 50, 100, 250, 500], \n",
    "         [np.power(np.sum(data_dict[ns]['Sz'], axis=1) - np.sum(data_dict[ns]['Sz_sample_sq'], axis=1), 2).sum() for ns in[10, 25, 50, 100, 250, 500]],\n",
    "        marker='s', label='sampling q')\n",
    "plt.plot([10, 25, 50, 100, 250, 500], \n",
    "         [np.power(np.sum(data_dict[ns]['Sz'], axis=1) - np.sum(data_dict[ns]['Sz_sample_nsq'], axis=1), 2).sum() for ns in[10, 25, 50, 100, 250, 500]],\n",
    "        marker='s', label='tracing q')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(r'Num Samples')\n",
    "plt.ylabel(r'$\\sum_\\beta \\left[\\sum_i (S_z^{exact}(i,\\beta) - S_z^{sampling}(i,\\beta))\\right]^2$')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}