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.

BoseHubbard	An extended Bose Hubbard model Hamiltonian operator, containing both on-site interactions and nearest-neighboring density-density interactions.
GraphOperator	A graph-based quantum operator.
LocalOperator	A custom local operator.
Ising	The Transverse-Field Ising Hamiltonian \(-h\sum_i \sigma_i^{(x)} +J\sum_{\langle i,j\rangle} \sigma_i^{(z)}\sigma_j^{(z)}\).
IsingJax
Heisenberg	The Heisenberg hamiltonian on a lattice.
PauliStrings	A Hamiltonian consisting of the sum of products of Pauli operators.
PauliStringsJax	Jax-compatible version of netket.operator.PauliStrings.
LocalLiouvillian	LocalLiouvillian super-operator, acting on the DoubledHilbert (tensor product) space ℋ⊗ℋ.

In the experimental submodule there is also a class to represent fermionic operators.

experimental.operator.FermionOperator2nd

A fermionic operator in \(2^{nd}\) quantization, using Numba for indexing.

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
SumOperator	This class implements the action of the _expect_kernel()-method of ContinuousOperator for a sum of ContinuousOperator objects.

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.

In the experimental submodule there are also easy-to-use constructors for common FermionOperator2nd.

experimental.operator.fermion.create	Builds the fermion creation operator \(\hat{a}^\dagger\) acting on the site-th of the Hilbert space hilbert.
experimental.operator.fermion.destroy	Builds the fermion destruction operator \(\hat{a}\) acting on the site-th of the Hilbert space hilbert.
experimental.operator.fermion.identity	Builds the \(\mathbb{I}\) identity operator.
experimental.operator.fermion.number	Builds the number operator \(\hat{a}^\dagger\hat{a}\) acting on the site-th of the Hilbert space hilbert.