netket.operator.Ising#
- class netket.operator.Ising[source]#
Bases:
IsingBase
The Transverse-Field Ising Hamiltonian \(-h\sum_i \sigma_i^{(x)} +J\sum_{\langle i,j\rangle} \sigma_i^{(z)}\sigma_j^{(z)}\).
This implementation is considerably faster than the Ising hamiltonian constructed by summing
LocalOperator
s.- Inheritance
- Attributes
- H#
Returns the Conjugate-Transposed operator
- J#
The magnitude of the hopping
- T#
Returns the transposed operator
- dtype#
The dtype of the matrix elements.
- edges#
The (N_conns, 2) matrix of edges on which the interaction term is non-zero.
- h#
The magnitude of the transverse field
- hilbert#
The hilbert space associated to this observable.
- is_hermitian#
A boolean stating whether this hamiltonian is hermitian.
- max_conn_size#
The maximum number of non zero ⟨x|O|x’⟩ for every x.
- 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=True)[source]#
Returns the complex-conjugate of this operator.
- Parameters:
concrete – if True returns a concrete operator and not a lazy wrapper
- Returns:
if concrete is not True, self or a lazy wrapper; the complex-conjugated operator otherwise
- 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:
x (
matrix
) – A matrix of shape (batch_size,hilbert.size) containing the batch of quantum numbers x.sections (
array
) – An array of size (batch_size) useful to unflatten the output of this function. See numpy.split for the meaning of sections.pad (
bool
) – no effect here
- Returns:
The connected states x’, flattened together in a single matrix. array: An array containing the matrix elements \(O(x,x')\) associated to each x’.
- Return type:
matrix
- get_conn_padded(x)[source]#
Finds the connected elements of the Operator.
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 (
ndarray
) – 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 states connected to x.
- 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 Numpy array.
- to_jax_operator()[source]#
Returns the jax-compatible version of this operator, which is an instance of
netket.operator.IsingJax
.- Return type:
- to_sparse()[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.
- Return type:
- Returns:
The sparse matrix representation of the operator.