netket.operator

The Operator module defines the common interfaces used to interact with quantum operators and super-operators, as well as several concrete implementations of different operators such as netket.hilbert.LocalOperator, netket.hilbert.Ising and others.

NetKet’s operators are all sub-classes of the abstract class netket.hilbert.AbstractOperator, which defines a small set of API respected by all implementations. The inheritance diagram for the class hierarchy of the Operators included with NetKet is shown below (you can click on the nodes in the graph to go to their API documentation page). Dashed nodes represent abstract classes that cannot be instantiated, while the others are concrete and they can be instantiated.

Abstract Classes

Below you find a list of all public classes defined in this module Those classes cannot be directly instantiated, but you can inherit from one of them if you want to define new hilbert spaces.

AbstractOperator	Abstract class for quantum Operators.
AbstractSuperOperator	Generic base class for super-operators acting on the tensor product (DoubledHilbert) space ℋ⊗ℋ, where ℋ is the physical space.
DiscreteOperator	This class is the base class for operators defined on a discrete Hilbert space.
DiscreteJaxOperator	Abstract base class for discrete operators that can be manipulated inside of jax function transformations.
ContinuousOperator	This class is the abstract base class for operators defined on a continuous Hilbert space.

Concrete Classes

Below you find a list of all concrete Operators that you can create on DiscreteHilbert spaces.

BoseHubbardJax
BoseHubbardNumba	An extended Bose Hubbard model Hamiltonian operator, containing both on-site interactions and nearest-neighboring density-density interactions.
GraphOperator	A graph-based quantum operator.
LocalOperatorJax	Jax implementation of an operator composed of a sum of local terms, each of which acts on a small number of sites.
LocalOperatorNumba	Numba implementation of an operator composed of a sum of local terms, each of which acts on a small number of sites.
IsingJax	Jax-based implementation of the Transverse-Field Ising Hamiltonian \(-h\sum_i \sigma_i^{(x)} +J\sum_{\langle i,j\rangle} \sigma_i^{(z)}\sigma_j^{(z)}\).
IsingNumba	The Transverse-Field Ising Hamiltonian \(-h\sum_i \sigma_i^{(x)} +J\sum_{\langle i,j\rangle} \sigma_i^{(z)}\sigma_j^{(z)}\).
Heisenberg	Constructs an Heisenberg operator given a hilbert space and a graph providing the connectivity of the lattice.
PauliStringsJax	Jax-compatible version of netket.operator.PauliStrings.
PauliStringsNumba	A Hamiltonian consisting of the sum of products of Pauli operators.
LocalLiouvillian	LocalLiouvillian super-operator, acting on the DoubledHilbert (tensor product) space ℋ⊗ℋ.

Fermions

Operators and functions to work with fermions are the following:

FermionOperator2ndJax	A fermionic operator in \(2^{nd}\) quantization using pure jax dark magic for indexing.
FermionOperator2ndNumba	A fermionic operator in \(2^{nd}\) quantization, using Numba for indexing.

In the experimental submodule there is also an implementation of a particle-number conserving operator which can be more efficient than the generic FermionOperator2ndJax.

experimental.operator.ParticleNumberConservingFermioperator2nd	Particle-number conserving fermionc operator
experimental.operator.ParticleNumberAndSpinConservingFermioperator2nd	Particle-number conserving and spin-Z-conserving fermionc operator
experimental.operator.FermiHubbardJax	Fermi-Hubbard Hamiltonian based on the generic ParticleNumberAndSpinConservingFermioperator2nd

Note in particular the pyscf module that can be used to convert molecules from pyscf to netket format. The support for PyScf is still experimental, and can be found in Fermions and PyScf

Continuous space operators

This is a list of operators that you can define on ContinuousHilbert spaces.

KineticEnergy	This is the kinetic energy operator (hbar = 1).
PotentialEnergy	Returns the local potential energy defined in afun

Permutation operators

Operators representing permutations, mainly used to express the lattice symmetries for wavefunction symmetrization in symmetries, as described in Representation theory in NetKet.

permutation.PermutationOperator	Permutation operator on a spin or boson space.
permutation.PermutationOperatorFermion	Operators corresponding to the permutation of the orbitals belonging to a second quantized fermionic space.
permutation.construct_permutation_operator	Return the appropriate permutation operator depending on the type of Hilbert space.

Internal operators

Operators used internally to implement symmetry representations. They are public but low-level; prefer the higher-level constructors in netket.symmetry.

SpinFlipOperator

Composing different operators together

Operators of different types, but acting on the same Hilbert space, can be combined by means of the operators described below. This is also useful to parametrize in a jax-friendly way time-dependent Hamiltonians.

SumOperator	Base class for sum of quantum operators.
ProductOperator	Base class for product of quantum operators.
EmbedOperator

Pre-defined operators

Those are easy-to-use constructors for a LocalOperator.

boson.create	Builds the boson creation operator \(\hat{a}^\dagger\) acting on the site-th of the Hilbert space hilbert.
boson.destroy	Builds the boson destruction operator \(\hat{a}\) acting on the site-th of the Hilbert space hilbert.
boson.identity	Builds the \(\mathbb{I}\) identity operator.
boson.number	Builds the number operator \(\hat{a}^\dagger\hat{a}\) acting on the site-th of the Hilbert space hilbert.
boson.proj	Builds the projector operator \(|n\rangle\langle n |\) acting on the site-th of the Hilbert space hilbert and collapsing on the state with n bosons.
spin.identity	Builds the \(\mathbb{I}\) identity operator.
spin.sigmax	Builds the \(\sigma^x\) operator acting on the site-th of the Hilbert space hilbert.
spin.sigmay	Builds the \(\sigma^y\) operator acting on the site-th of the Hilbert space hilbert.
spin.sigmaz	Builds the \(\sigma^z\) operator acting on the site-th of the Hilbert space hilbert.
spin.sigmap	Builds the \(\sigma^{+} = \frac{1}{2}(\sigma^x + i \sigma^y)\) operator acting on the site-th of the Hilbert space hilbert.
spin.sigmam	Builds the \(\sigma^{-} = \frac{1}{2}(\sigma^x - i \sigma^y)\) operator acting on the site-th of the Hilbert space hilbert.
fermion.create	Builds the fermion creation operator \(\hat{a}^\dagger\) acting on the site-th of the Hilbert space hilbert.
fermion.destroy	Builds the fermion destruction operator \(\hat{a}\) acting on the site-th of the Hilbert space hilbert.
fermion.number	Builds the number operator \(\hat{a}^\dagger\hat{a}\) acting on the site-th of the Hilbert space hilbert.

Utilities

to_sparse_cached

Returns the sparse matrix representation of the operator with caching.

_local_operator.LocalOperator
_local_operator.LocalOperatorBase	Base implementation of an operator composed of a sum of local terms, each of which acts on a small number of sites.
_ising.Ising
_ising.IsingBase	Jax-based implementation of the Transverse-Field Ising Hamiltonian \(-h\sum_i \sigma_i^{(x)} +J\sum_{\langle i,j\rangle} \sigma_i^{(z)}\sigma_j^{(z)}\).
_pauli_strings.PauliStrings
_pauli_strings.PauliStringsBase	A Hamiltonian consisting of the sum of products of Pauli operators, acting on any number of sites.
_fermion2nd.FermionOperator2nd
_fermion2nd.FermionOperator2ndBase	A fermionic operator in \(2^{nd}\) quantization.
_sum.SumContinuousOperator	This class implements the action of the _expect_kernel()-method of ContinuousOperator for a sum of ContinuousOperator objects.
_sum.SumGenericOperator
_sum.SumDiscreteJaxOperator
_sum.SumDiscreteOperator
_prod.ProductGenericOperator
_prod.ProductDiscreteOperator
_prod.ProductDiscreteJaxOperator