# Copyright 2021 The NetKet Authors - All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from scipy import sparse as _sparse
from netket.utils.types import DType as _DType
from netket.hilbert import AbstractHilbert as _AbstractHilbert
from ._local_operator import LocalOperator as _LocalOperator
[docs]def destroy(
hilbert: _AbstractHilbert, site: int, dtype: _DType = float
) -> _LocalOperator:
"""
Builds the boson destruction operator :math:`\\hat{a}` acting on the `site`-th of
the Hilbert space `hilbert`.
If `hilbert` is a non-Bosonic space of local dimension M, it is considered
as a bosonic space of local dimension M.
Args:
hilbert: The hilbert space
site: the site on which this operator acts
Returns:
The resulting Local Operator
"""
import numpy as np
N = hilbert.size_at_index(site)
D = np.array([np.sqrt(m) for m in np.arange(1, N)])
mat = np.diag(D, 1)
mat = _sparse.coo_matrix(mat)
return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def create(
hilbert: _AbstractHilbert, site: int, dtype: _DType = float
) -> _LocalOperator:
"""
Builds the boson creation operator :math:`\\hat{a}^\\dagger` acting on the `site`-th
of the Hilbert space `hilbert`.
If `hilbert` is a non-Bosonic space of local dimension M, it is considered
as a bosonic space of local dimension M.
Args:
hilbert: The hilbert space
site: the site on which this operator acts
Returns:
The resulting Local Operator
"""
import numpy as np
N = hilbert.size_at_index(site)
D = np.array([np.sqrt(m) for m in np.arange(1, N)])
mat = np.diag(D, -1)
mat = _sparse.coo_matrix(mat)
return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def number(
hilbert: _AbstractHilbert, site: int, dtype: _DType = float
) -> _LocalOperator:
"""
Builds the number operator :math:`\\hat{a}^\\dagger\\hat{a}` acting on the
`site`-th of the Hilbert space `hilbert`.
If `hilbert` is a non-Bosonic space of local dimension M, it is considered
as a bosonic space of local dimension M.
Args:
hilbert: The hilbert space
site: the site on which this operator acts
Returns:
The resulting Local Operator
"""
import numpy as np
N = hilbert.size_at_index(site)
D = np.array([m for m in np.arange(0, N)])
mat = np.diag(D, 0)
mat = _sparse.coo_matrix(mat)
return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def proj(
hilbert: _AbstractHilbert, site: int, n: int, dtype: _DType = float
) -> _LocalOperator:
"""
Builds the projector operator :math:`|n\\rangle\\langle n |` acting on the
`site`-th of the Hilbert space `hilbert` and collapsing on the state with `n`
bosons.
If `hilbert` is a non-Bosonic space of local dimension M, it is considered
as a bosonic space of local dimension M.
Args:
hilbert: The hilbert space
site: the site on which this operator acts
n: the state on which to project
Returns:
the resulting operator
"""
import numpy as np
N = hilbert.size_at_index(site)
if n >= N:
raise ValueError("Cannot project on a state above the cutoff.")
D = np.array([0 for m in np.arange(0, N)])
D[n] = 1
mat = np.diag(D, 0)
mat = _sparse.coo_matrix(mat)
return _LocalOperator(hilbert, mat, [site], dtype=dtype)
