def onebody_sum_mpo(terms, output_label=None):
"""
Construct an MPO from a sum of onebody operators, using the recipe from
the Supplemental Material of [1]_ (Eqs. (3) and (4))
Parameters
---------
terms : list
A list containing the terms in the sum. Each term should be 2D
array-like, e.g., a rank-two Tensor or numpy array.
output_label : str, optional
Specify the label corresponding to the output index. Must be the same
for each element of `terms`. If not specified the first index is taken
to be the output index.
Returns
------
MatrixProductOperator
References
----------
.. [1] E. Sanchez-Burillo et al., Phys. Rev. Lett. 113, 263604 (2014)
"""
tensors = []
for i, term1 in enumerate(terms):
if output_label is not None:
term = term1.copy()
term.move_index(output_label, 0)
else:
term = term1
if i == 0:
B = np.zeros(shape=term.shape + (2, ), dtype=complex)
for k in range(term.shape[0]):
for l in range(term.shape[1]):
B[k, l, :] = [term[k, l], k == l]
tensors.append(tnc.Tensor(B, ['physout', 'physin', 'right']))
elif i == len(terms) - 1:
B = np.zeros(shape=term.shape + (2, ), dtype=complex)
for k in range(term.shape[0]):
for l in range(term.shape[1]):
B[k, l, :] = [k == l, term[k, l]]
tensors.append(tnc.Tensor(B, ['physout', 'physin', 'left']))
else:
B = np.zeros(shape=term.shape + (2, 2), dtype=complex)
for k in range(term.shape[0]):
for l in range(term.shape[1]):
B[k, l, :, :] = [[k == l, 0], [term[k, l], k == l]]
tensors.append(
tnc.Tensor(B, ['physout', 'physin', 'left', 'right']))
return onedim.MatrixProductOperator(tensors,
left_label='left',
right_label='right',
physin_label='physin',
physout_label='physout')
def init_mps_logical(nsites, basis_state, physdim, left_label='left',
right_label='right', phys_label='phys'):
"""
Create an MPS with `nsites` sites in the logical basis state |ijk..l>.
Parameters
----------
nsites : int
basis_state : int or list of ints
Site `i` will be in the state |`basis_state[i]`> (or simply
|`basis_state`> if a single int is provided).
physdim : int or list of ints
left_label : str
right_label : str
phys_label : str
"""
if not np.iterable(physdim):
physdim = [physdim] * nsites
tensors = []
for j in range(nsites):
t = np.zeros(physdim[j])
t[basis_state[j]] = 1.0
t = tnc.Tensor(t.reshape(physdim[j], 1, 1), [phys_label, left_label,
right_label])
tensors.append(t)
return onedim.MatrixProductState(tensors, left_label=left_label,
right_label=right_label, phys_label=phys_label)
def init_mps_allzero(nsites, physdim, left_label='left',
right_label='right', phys_label='phys'):
"""
Create an MPS with `nsites` sites in the "all zero" state |00..0>.
Parameters
----------
nsites : int
physdim : int or list of ints
left_label : str
right_label : str
phys_label : str
"""
if not np.iterable(physdim):
physdim = [physdim] * nsites
tensors = []
for j in range(nsites):
t = np.zeros(physdim[j])
t[0] = 1.0
t = tnc.Tensor(t.reshape(physdim[j], 1, 1), [phys_label, left_label,
right_label])
tensors.append(t)
return onedim.MatrixProductState(tensors, left_label=left_label,
right_label=right_label, phys_label=phys_label)
def init_mps_random(nsites,
physdim,
bonddim=1,
left_label='left',
right_label='right',
phys_label='phys'):
"""
Create an MPS with `nsites` sites and random tensors with physical
dimensions given by `physdim` and bond dimensions given by
`bonddim`. Open boundary conditions are used. The MPS is not normalized.
Parameters
----------
nsites : int
physdim : int or list of ints
bonddim : int or list of ints, optional
The nth element of `bonddim` determines the right and left index of
the tensors at sites n and n+1, respectively. The length of `bonddim`
should be `nsites`-1. If `bonddim` is an int this is this is used for
all bonds.
left_label : str
right_label : str
phys_label : str
"""
if not np.iterable(physdim):
physdim = [physdim] * nsites
if not np.iterable(bonddim):
bonddim = [bonddim] * (nsites - 1)
bonddim = [1] + bonddim + [1]
tensors = []
for i in range(nsites):
rt = tnc.Tensor(np.random.rand(physdim[i], bonddim[i], bonddim[i + 1]),
[phys_label, left_label, right_label])
# Normalize matrix to avoid norm blowing up
U, S, V = tnc.tensor_svd(rt, [phys_label, left_label])
S.data = S.data / S.data[0, 0]
rt = U["svd_in", ] * S["svd_out", ]
rt = rt["svd_in", ] * V["svd_out", ]
tensors.append(rt)
return onedim.MatrixProductState(tensors,
left_label=left_label,
right_label=right_label,
phys_label=phys_label)