Source code for netket.operator.spin

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#    http://www.apache.org/licenses/LICENSE-2.0
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from netket.utils.types import DType as _DType

from netket.hilbert import AbstractHilbert as _AbstractHilbert

from ._local_operator import LocalOperator as _LocalOperator


[docs]def sigmax( hilbert: _AbstractHilbert, site: int, dtype: _DType = float ) -> _LocalOperator: """ Builds the :math:`\\sigma^x` operator acting on the `site`-th of the Hilbert space `hilbert`. If `hilbert` is a non-Spin space of local dimension M, it is considered as a (M-1)/2 - spin space. :param hilbert: The hilbert space :param site: the site on which this operator acts :return: a nk.operator.LocalOperator """ import numpy as np N = hilbert.size_at_index(site) S = (N - 1) / 2 D = [np.sqrt((S + 1) * 2 * a - a * (a + 1)) for a in np.arange(1, N)] mat = np.diag(D, 1) + np.diag(D, -1) return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def sigmay( hilbert: _AbstractHilbert, site: int, dtype: _DType = complex ) -> _LocalOperator: """ Builds the :math:`\\sigma^y` operator acting on the `site`-th of the Hilbert space `hilbert`. If `hilbert` is a non-Spin space of local dimension M, it is considered as a (M-1)/2 - spin space. :param hilbert: The hilbert space :param site: the site on which this operator acts :return: a nk.operator.LocalOperator """ import numpy as np import netket.jax as nkjax if not nkjax.is_complex_dtype(dtype): import jax.numpy as jnp import warnings old_dtype = dtype dtype = jnp.promote_types(complex, old_dtype) warnings.warn( np.ComplexWarning( f"A complex dtype is required (dtype={old_dtype} specified). " f"Promoting to dtype={dtype}." ) ) N = hilbert.size_at_index(site) S = (N - 1) / 2 D = np.array([1j * np.sqrt((S + 1) * 2 * a - a * (a + 1)) for a in np.arange(1, N)]) mat = np.diag(D, -1) + np.diag(-D, 1) return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def sigmaz( hilbert: _AbstractHilbert, site: int, dtype: _DType = float ) -> _LocalOperator: """ Builds the :math:`\\sigma^z` operator acting on the `site`-th of the Hilbert space `hilbert`. If `hilbert` is a non-Spin space of local dimension M, it is considered as a (M-1)/2 - spin space. :param hilbert: The hilbert space :param site: the site on which this operator acts :return: a nk.operator.LocalOperator """ import numpy as np N = hilbert.size_at_index(site) S = (N - 1) / 2 D = np.array([2 * m for m in np.arange(S, -(S + 1), -1)]) mat = np.diag(D, 0) return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def sigmam( hilbert: _AbstractHilbert, site: int, dtype: _DType = float ) -> _LocalOperator: """ Builds the :math:`\\sigma^{-} = \\frac{1}{2}(\\sigma^x - i \\sigma^y)` operator acting on the `site`-th of the Hilbert space `hilbert`. If `hilbert` is a non-Spin space of local dimension M, it is considered as a (M-1)/2 - spin space. :param hilbert: The hilbert space :param site: the site on which this operator acts :return: a nk.operator.LocalOperator """ import numpy as np N = hilbert.size_at_index(site) S = (N - 1) / 2 S2 = (S + 1) * S D = np.array([np.sqrt(S2 - m * (m - 1)) for m in np.arange(S, -S, -1)]) mat = np.diag(D, -1) return _LocalOperator(hilbert, mat, [site], dtype=dtype)
[docs]def sigmap( hilbert: _AbstractHilbert, site: int, dtype: _DType = float ) -> _LocalOperator: """ Builds the :math:`\\sigma^{+} = \\frac{1}{2}(\\sigma^x + i \\sigma^y)` operator acting on the `site`-th of the Hilbert space `hilbert`. If `hilbert` is a non-Spin space of local dimension M, it is considered as a (M-1)/2 - spin space. :param hilbert: The hilbert space :param site: the site on which this operator acts :return: a nk.operator.LocalOperator """ import numpy as np N = hilbert.size_at_index(site) S = (N - 1) / 2 S2 = (S + 1) * S D = np.array([np.sqrt(S2 - m * (m + 1)) for m in np.arange(S - 1, -(S + 1), -1)]) mat = np.diag(D, 1) return _LocalOperator(hilbert, mat, [site], dtype=dtype)