netket.experimental.operator.ParticleNumberConservingFermioperator2nd#
- class netket.experimental.operator.ParticleNumberConservingFermioperator2nd[source]#
Bases:
DiscreteJaxOperatorParticle-number conserving fermionc operator
\[\hat H = w + \sum_{ij} w_{ij} \hat c_i^\dagger \hat c_j + \sum_{ijkl} w_{ijkl} \hat c_i^\dagger \hat c_j^\dagger \hat c_k \hat c_l + \sum_{ijklmn} w_{ijklmn} \hat c_i^\dagger \hat c_j^\dagger c_k^\dagger \hat c_l \hat c_m \hat c_n + \dots\]To be used with netket.hilbert.SpinOrbitalFermions with a fixed number of fermions.
It uses a custom sparse internal representation, please refer to the docstrings of prepare_data and prepare_data_diagonal for details.
- We provide several factory methods to create this operator:
- ParticleNumberConservingFermioperator2nd.from_fermionoperator2nd:
Conversion form FermionOperator2nd/FermionOperator2ndJax
- ParticleNumberConservingFermioperator2nd.from_sparse_arrays:
From sparse arrays (w, w_ij, w_ijkl, w_ijklmn, …)
- ParticleNumberConservingFermioperator2nd.from_pyscf_molecule:
From pyscf
Furthermore it can be converted to FermionOperator2nd/FermionOperator2ndJax using the .to_fermionoperator2nd() method.
- Inheritance
- Attributes
- H#
Returns the Conjugate-Transposed operator
- T#
Returns the transposed operator
- dtype#
- hilbert#
The hilbert space associated to this observable.
- is_hermitian#
- max_conn_size#
- Methods
-
- collect()[source]#
Returns a guaranteed concrete instance of an operator.
As some operations on operators return lazy wrappers (such as transpose, hermitian conjugate…), this is used to obtain a guaranteed non-lazy operator.
- Return type:
- conjugate(*, concrete=False)[source]#
Returns the complex-conjugate of this operator.
- Parameters:
concrete – if True returns a concrete operator and not a lazy wrapper
- Return type:
- Returns:
if concrete is not True, self or a lazy wrapper; the complex-conjugated operator otherwise
- classmethod from_fermionoperator2nd(ha, **kwargs)[source]#
Convert from FermionOperator2nd
- Parameters:
ha (
FermionOperator2ndJax) – the original FermionOperator2nd/FermionOperator2ndJax operator
Throws an error if the original operator is not particle-number conserving.
- classmethod from_pyscf_molecule(mol, mo_coeff, cutoff=1e-11, **kwargs)[source]#
Constructs the operator from a pyscf molecule
- Parameters:
mol (pyscf.gto.mole.Mole) – pyscf molecule
mo_coeff (
Union[ndarray,Array]) – molecular orbital coefficients, e.g. obtained from a HF calculationcutoff (
float) – cutoff to use when converting the operators to the internal format. Use a small but nonzero number, to allow for internal equality checks between arrays.
- classmethod from_sparse_arrays(hilbert, operators, **kwargs)[source]#
initialize from a list of arrays
- Parameters:
hilbert (
SpinOrbitalFermions) – hilbert spaceoperators (
list[Union[ndarray,Array,COO]]) – list of dense or sparse arrays, each representing an m-body operator for different mcutoff – cutoff to use when converting the operators to the internal format. Use a small but nonzero number, to allow for internal equality checks between arrays.
Example: Given an array A of rank 2m with shape (n_orbitals,)*(2m) this initializes the operator
\[\hat A = \sum_{i_1,\dots,i_m, j_1,\dots,j_m} A_{i_1 \cdots i_m j_1 \cdots j_m} \hat c_{i_1}^\dagger \cdots \hat c_{i_m}^\dagger \hat c_{j_1} \cdots \hat c_{j_m}\]
- get_conn(x)[source]#
Finds the connected elements of the Operator. Starting from a given quantum number x, it finds all other quantum numbers x’ such that the matrix element \(O(x,x')\) is different from zero. In general there will be several different connected states x’ satisfying this condition, and they are denoted here \(x'(k)\), for \(k=0,1...N_{\mathrm{connected}}\).
- Parameters:
x (
ndarray) – An array of shape (hilbert.size, ) containing the quantum numbers x.- Returns:
The connected states x’ of shape (N_connected,hilbert.size) array: An array containing the matrix elements \(O(x,x')\) associated to each x’.
- Return type:
matrix
- Raises:
ValueError – If the given quantum number is not compatible with the hilbert space.
- get_conn_flattened(x, sections, pad=False)[source]#
Finds the connected elements of the Operator.
Starting from a given quantum number \(x\), it finds all other quantum numbers \(x'\) such that the matrix element \(O(x,x')\) is different from zero. In general there will be several different connected states \(x'\) satisfying this condition, and they are denoted here \(x'(k)\), for \(k=0,1...N_{\mathrm{connected}}\).
This is a batched version, where x is a matrix of shape
(batch_size,hilbert.size).- Parameters:
- Returns:
- The connected states x’, flattened together in
a single matrix. An array containing the matrix elements \(O(x,x')\) associated to each x’.
- Return type:
(matrix, array)
- get_conn_padded(x)[source]#
Finds the connected elements of the Operator. This method can be executed inside of a Jax function transformation.
Starting from a batch of quantum numbers \(x={x_1, ... x_n}\) of size \(B \times M\) where \(B\) size of the batch and \(M\) size of the hilbert space, finds all states \(y_i^1, ..., y_i^K\) connected to every \(x_i\).
Returns a matrix of size \(B \times K_{max} \times M\) where \(K_{max}\) is the maximum number of connections for every \(y_i\).
- Parameters:
x – A N-tensor of shape \((...,hilbert.size)\) containing the batch/batches of quantum numbers \(x\).
- Returns:
The connected states x’, in a N+1-tensor and an N-tensor containing the matrix elements \(O(x,x')\) associated to each x’ for every batch.
- Return type:
(x_primes, mels)
- n_conn(x, out=None)[source]#
Return the number of (non-zero) connected entries to x.
Warning
This is not the True number of connected entries, because some elements might appear twice (however this should not be too common.)
Note that this deviates from the Numba implementation, and can generally return a smaller number of connected entries.
- Parameters:
x (
matrix) – A matrix of shape (batch_size,hilbert.size) containing the batch of quantum numbers x.out (
array) – If None an output array is allocated.
- Returns:
The number of connected states x’ for each x[i].
- Return type:
array
- to_dense()[source]#
Returns the dense matrix representation of the operator. Note that, in general, the size of the matrix is exponential in the number of quantum numbers, and this operation should thus only be performed for low-dimensional Hilbert spaces or sufficiently sparse operators.
This method requires an indexable Hilbert space.
- Return type:
- Returns:
The dense matrix representation of the operator as a jax Array.
- to_fermionoperator2nd(_cls=<class 'netket.operator._fermion2nd.jax.FermionOperator2ndJax'>)[source]#
Convert to FermionOperator2ndJax
- Return type:
FermionOperator2ndJax
- to_jax_operator()[source]#
Return the JAX version of this operator.
If this is a JAX operator does nothing.
- Return type:
- to_sparse(jax_=False)[source]#
Returns the sparse matrix representation of the operator. Note that, in general, the size of the matrix is exponential in the number of quantum numbers, and this operation should thus only be performed for low-dimensional Hilbert spaces or sufficiently sparse operators.
This method requires an indexable Hilbert space.