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Merge pull request #21 from tenpy/add_common_sector_names
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Add common sector names
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@Jakob-Unfried
Jakob-Unfried authored Dec 5, 2024
2 parents 3f7d455 + 62bcad4 commit beafd2c
Showing 1 changed file with 58 additions and 15 deletions.
73 changes: 58 additions & 15 deletions cyten/symmetries.py
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Original file line number Diff line number Diff line change
Expand Up @@ -24,7 +24,7 @@
'SU2Symmetry', 'SUNSymmetry',
# anyons
'FermionParity', 'FibonacciAnyonCategory', 'IsingAnyonCategory', 'SU3_3AnyonCategory',
'QuantumDoubleZNAnyonCategory', 'SU2_kAnyonCategory', 'ZNAnyonCategory',
'QuantumDoubleZNAnyonCategory', 'ToricCodeCategory', 'SU2_kAnyonCategory', 'ZNAnyonCategory',
'ZNAnyonCategory2',
# concrete instances
'no_symmetry', 'u1_symmetry', 'z2_symmetry', 'z3_symmetry', 'z4_symmetry', 'z5_symmetry', 'z6_symmetry',
Expand Down Expand Up @@ -1240,6 +1240,9 @@ class SU2Symmetry(GroupSymmetry):
"""

fusion_tensor_dtype = Dtype.float64
spin_zero = as_immutable_array(np.array([0], dtype=int))
spin_half = as_immutable_array(np.array([1], dtype=int))
spin_one = as_immutable_array(np.array([2], dtype=int))

def __init__(self, descriptive_name: str | None = None):
GroupSymmetry.__init__(self, fusion_style=FusionStyle.multiple_unique, trivial_sector=np.array([0], dtype=int),
Expand Down Expand Up @@ -1891,6 +1894,8 @@ class FermionParity(Symmetry):
_one_2D_float = as_immutable_array(np.ones((1, 1), dtype=float))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))
_one_4D_float = as_immutable_array(np.ones((1, 1, 1, 1), dtype=float))
even = as_immutable_array(np.array([0], dtype=int))
odd = as_immutable_array(np.array([1], dtype=int))

def __init__(self):
Symmetry.__init__(self, fusion_style=FusionStyle.single, braiding_style=BraidingStyle.fermionic,
Expand Down Expand Up @@ -1994,8 +1999,9 @@ class ZNAnyonCategory(Symmetry):
_one_1D = as_immutable_array(np.ones((1,), dtype=int))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))

def __init__(self, N: int, n: int):
def __init__(self, N: int, n: int, descriptive_name: str | None = None):
assert type(N) == int
assert N > 1
assert type(n) == int
self.N = N
self.n = n % N
Expand All @@ -2004,8 +2010,8 @@ def __init__(self, N: int, n: int):
fusion_style=FusionStyle.single,
braiding_style=BraidingStyle.anyonic,
trivial_sector=np.array([0], dtype=int),
group_name='ZNAnyonCategory',
num_sectors=N, descriptive_name=None)
group_name=f'ℤ_{N}^{n} anyon category',
num_sectors=N, descriptive_name=descriptive_name)

def is_valid_sector(self, a: Sector) -> bool:
return getattr(a, 'shape', ()) == (1,) and 0 <= a[0] < self.N
Expand Down Expand Up @@ -2033,7 +2039,8 @@ def batch_qdim(self, a: SectorArray) -> np.ndarray:
return np.ones((len(a),), int)

def __repr__(self):
return f'ZNAnyonCategory(N={self.N}, n={self.n})'
name_str = '' if self.descriptive_name is None else f'"{self.descriptive_name}"'
return f'ZNAnyonCategory({self.N}, {self.n}, {name_str})'

def is_same_symmetry(self, other) -> bool:
return isinstance(other, ZNAnyonCategory) and other.N == self.N and other.n == self.n
Expand Down Expand Up @@ -2086,8 +2093,9 @@ class ZNAnyonCategory2(Symmetry):
_one_1D = as_immutable_array(np.ones((1,), dtype=int))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))

def __init__(self, N: int, n: int):
def __init__(self, N: int, n: int, descriptive_name: str | None = None):
assert type(N) == int
assert N > 1
assert N % 2 == 0
assert type(n) == int
self.N = N
Expand All @@ -2097,8 +2105,8 @@ def __init__(self, N: int, n: int):
fusion_style=FusionStyle.single,
braiding_style=BraidingStyle.anyonic,
trivial_sector=np.array([0], dtype=int),
group_name='ZNAnyonCategory2',
num_sectors=N, descriptive_name=None)
group_name=f'ℤ_{N}^({n}+1/2) anyon category',
num_sectors=N, descriptive_name=descriptive_name)

def is_valid_sector(self, a: Sector) -> bool:
return getattr(a, 'shape', ()) == (1,) and 0 <= a < self.N
Expand Down Expand Up @@ -2126,7 +2134,8 @@ def batch_qdim(self, a: SectorArray) -> np.ndarray:
return np.ones((len(a),), int)

def __repr__(self):
return f'ZNAnyonCategory2(N={self.N}, n={self.n})'
name_str = '' if self.descriptive_name is None else f'"{self.descriptive_name}"'
return f'ZNAnyonCategory2({self.N}, {self.n}, {name_str})'

def is_same_symmetry(self, other) -> bool:
return isinstance(other, ZNAnyonCategory2) and other.N == self.N and other.n == self.n
Expand Down Expand Up @@ -2161,7 +2170,7 @@ def all_sectors(self) -> SectorArray:


class QuantumDoubleZNAnyonCategory(Symmetry):
"""Doubled abelian anyon category with fusion rules corresponding to the Z_N group;
"""Doubled abelian anyon category with fusion rules corresponding to the Z_N x Z_N group;
also written as :math:`D(Z_N)`.
Allowed sectors are 1D arrays with two integers between `0` and `N-1`.
Expand All @@ -2172,16 +2181,17 @@ class QuantumDoubleZNAnyonCategory(Symmetry):
_one_2D = as_immutable_array(np.ones((1, 1), dtype=int))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))

def __init__(self, N: int):
def __init__(self, N: int, descriptive_name: str | None = None):
assert type(N) == int
assert N > 1
self.N = N
self._phase = np.exp(2j * np.pi / self.N)
Symmetry.__init__(self,
fusion_style=FusionStyle.single,
braiding_style=BraidingStyle.anyonic,
trivial_sector=np.array([0, 0], dtype=int),
group_name='QuantumDoubleZNAnyonCategory',
num_sectors=N**2, descriptive_name=None)
group_name=f'D(ℤ_{N})',
num_sectors=N**2, descriptive_name=descriptive_name)

def is_valid_sector(self, a: Sector) -> bool:
return getattr(a, 'shape', ()) == (2,) and np.all(0 <= a) and np.all(a < self.N)
Expand Down Expand Up @@ -2209,7 +2219,8 @@ def batch_qdim(self, a: SectorArray) -> np.ndarray:
return np.ones((len(a),), int)

def __repr__(self):
return f'QuantumDoubleZNAnyonCategory(N={self.N})'
name_str = '' if self.descriptive_name is None else f'"{self.descriptive_name}"'
return f'QuantumDoubleZNAnyonCategory({self.N}, {name_str})'

def is_same_symmetry(self, other) -> bool:
return isinstance(other, QuantumDoubleZNAnyonCategory) and other.N == self.N
Expand Down Expand Up @@ -2244,6 +2255,28 @@ def all_sectors(self) -> SectorArray:
return np.dstack(np.meshgrid(x, x)).reshape(-1, 2)


class ToricCodeCategory(QuantumDoubleZNAnyonCategory):
"""Toric code anyon category. Essentially equivalent to `QuantumDoubleZNAnyonCategory(N=2)`.
The allowed sectors are 1D arrays with two integers between `0` and `1`,
`[0, 0]`, `[0, 1]`, `[1, 0]`, `[1, 1]`, which are known as vacuum, electric charge,
magnetic flux and fermion, respectively.
The electric charges and magnetic fluxes are mutual semions and self-bosons.
"""
vacuum = as_immutable_array(np.array([0, 0], dtype=int))
electric_charge = as_immutable_array(np.array([0, 1], dtype=int))
magnetic_flux = as_immutable_array(np.array([1, 0], dtype=int))
fermion = as_immutable_array(np.array([1, 1], dtype=int))

def __init__(self, descriptive_name: str | None = None):
super().__init__(2, descriptive_name)

def __repr__(self):
name_str = '' if self.descriptive_name is None else f'"{self.descriptive_name}"'
return f'ToricCodeCategory({name_str})'


class FibonacciAnyonCategory(Symmetry):
"""Category describing Fibonacci anyons.
Expand All @@ -2268,6 +2301,8 @@ class FibonacciAnyonCategory(Symmetry):
_r = as_immutable_array(np.expand_dims([np.exp(-4j*np.pi/5), np.exp(3j*np.pi/5)], axis=1))
_one_1D = as_immutable_array(np.ones((1,), dtype=int))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))
vacuum = as_immutable_array(np.array([0], dtype=int))
tau = as_immutable_array(np.array([1], dtype=int))

def __init__(self, handedness = 'left'):
assert handedness in ['left', 'right']
Expand Down Expand Up @@ -2366,6 +2401,9 @@ class IsingAnyonCategory(Symmetry):
}
_one_1D = as_immutable_array(np.ones((1,), dtype=int))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))
vacuum = as_immutable_array(np.array([0], dtype=int))
sigma = as_immutable_array(np.array([1], dtype=int))
psi = as_immutable_array(np.array([2], dtype=int))

def __init__(self, nu: int = 1):
assert nu % 2 == 1
Expand Down Expand Up @@ -2481,11 +2519,16 @@ class SU2_kAnyonCategory(Symmetry):
"""
_one_1D = as_immutable_array(np.ones((1,), dtype=int))
_one_4D = as_immutable_array(np.ones((1, 1, 1, 1), dtype=int))
spin_zero = as_immutable_array(np.array([0], dtype=int))
spin_half = as_immutable_array(np.array([1], dtype=int))

def __init__(self, k: int, handedness = 'left'):
assert type(k) == int
assert k >= 1
assert handedness in ['left', 'right']
self.k = k
if k >= 2:
self.spin_one = as_immutable_array(np.array([2], dtype=int))
self.handedness = handedness
self._q = np.exp(2j * np.pi / (k + 2))

Expand Down Expand Up @@ -2833,7 +2876,7 @@ def all_sectors(self) -> SectorArray:
u1_symmetry = U1Symmetry()
fermion_parity = FermionParity()
semion_category = ZNAnyonCategory2(2, 0)
toric_code_category = QuantumDoubleZNAnyonCategory(2)
toric_code_category = ToricCodeCategory()
double_semion_category = ProductSymmetry([ZNAnyonCategory2(2, 0), ZNAnyonCategory2(2, 1)])
fibonacci_anyon_category = FibonacciAnyonCategory(handedness='left')
ising_anyon_category = IsingAnyonCategory(nu=1)

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