def domain_wall_indicator(i, basis, bc, check_symm=True, dtype=np.float64):
"""Local operator d which indicates (0 or 1) whether there is a domain wall (assuming a Z2 crytstal) to the right of site i.
d = (1 - n_i)(1-n_i+1) + n_i n_i+1"""
if not isinstance(basis, boson_basis_1d):
raise TypeError("Expecting 1d boson basis")
L = basis.L
if bc == 'open' and i == (L - 1):
return 0 * identity(basis)
n1 = n_op(i, basis, check_symm=check_symm, dtype=dtype)
n2 = n_op((i + 1) % L, basis, check_symm=check_symm, dtype=dtype)
return identity(basis) - (n1 + n2) + 2 * n1 * n2
def domain_wall_Z3_indicator(i, basis, bc, check_symm=True, dtype=np.float64):
"""Local operator d which indicates (0 or 1) whether there is a domain wall (assuming a Z2 crytstal) to the right of site i.
d = (1 - n_i)(1-n_i+1)"""
if not is_hcb_basis(basis):
raise TypeError("Expecting 1d boson basis")
L = basis.L
if bc == 'open' and (i == (L - 1) or i == 0):
return 0 * identity(basis)
n0 = n_op((i - 1) % L, basis, check_symm=check_symm, dtype=dtype)
n1 = n_op(i, basis, check_symm=check_symm, dtype=dtype)
n2 = n_op((i + 1) % L, basis, check_symm=check_symm, dtype=dtype)
I = identity(basis)
return (I - n0) * (I - n1) * (I - n2)
def proj_blockade_loc(i, basis, bc='periodic'):
""" Returns a local blockade projector defined on link i, i.e. between sites i, i+1.
Nonzero when at most one of those sites is excited.
Note that it's defined on the global hilbert space"""
if not isinstance(basis, boson_basis_1d):
raise TypeError("Expecting 1d boson basis input")
L = basis.L
#for open conditions, there's no constraint between 1st and last links
if bc == 'open' and i == (L - 1):
return identity(basis)
return identity(basis) - n2_op(
i, (i + 1) % L, L, basis=basis, check_symm=False)
def domain_wall_Z3_population(basis, bc, check_symm=True, dtype=np.float64):
if not is_hcb_basis(basis):
raise TypeError("Expecting 1d boson basis")
L = basis.L
Nd = 0 * identity(basis)
for ii in range(L):
Nd = Nd + domain_wall_Z3_indicator(
ii, basis, bc, check_symm=check_symm, dtype=dtype)
return Nd
def proj_blockade(basis, bc='periodic'):
""" Returns a global projector onto the blockade subspace.
(a next-nearest neighbor blockade)
basis = hcb basis
"""
if not isinstance(basis, boson_basis_1d):
raise TypeError("Expecting 1d boson basis input")
Pi = identity(basis)
L = basis.L
for i in range(L):
Pi = Pi * proj_blockade_loc(i, basis, bc=bc)
return Pi