netket.sampler.rules.FermionHopRule

netket.sampler.rules.FermionHopRule#

class netket.sampler.rules.FermionHopRule[source]#

Bases: ExchangeRule

Hopping rule for particles on a lattice.

Works similarly to netket.sampler.rules.ExchangeRule, but takes into account that only occupied orbitals can be exchanged with unoccupied ones.

This sampler conserves the number of particles.

Inheritance
Inheritance diagram of netket.sampler.rules.FermionHopRule
__init__(hilbert, *, clusters=None, graph=None, d_max=1, spin_symmetric=True)[source]#

Constructs the FermionHopRule.

Particles are only exchanged between modes where the particle number is different. For fermions, only occupied orbitals can be exchanged with unoccupied ones.

You can pass either a list of clusters or a netket graph object to determine the clusters to exchange.

Parameters:

  • hilbert – The hilbert space to be sampled.

  • clusters (list[tuple[int, int]] | None) – The list of clusters that can be exchanged. This should be a list of 2-tuples containing two integers. Every tuple is an edge, or cluster of sites to be exchanged.

  • graph (AbstractGraph | None) – A graph, from which the edges determine the clusters that can be exchanged.

  • d_max (int) – Only valid if a graph is passed in. The maximum distance between two sites

  • spin_symmetric (bool) – (default True) If spin_symmetric, the graph must encode the connectivity between the first N physical sites having same spin, and it is replicated using netket.graph.disjoint_union() other every spin subsector. This option conserves the number of fermions per spin subsector. If the graph does not have a number of sites equal to the number of orbitals in the hilbert space, this flag has no effect.

Attributes
clusters: jax.Array#

2-Dimensional tensor \(T_{i,j}\) of shape \(N_\text{clusters}\times 2\) where the first dimension runs over the list of 2-site clusters and the second dimension runs over the 2 sites of those clusters.

The Exchange rule will swap the two sites of a random row of this matrix at every Metropolis step.

Methods
init_state(sampler, machine, params, key)[source]#

Initialises the optional internal state of the Metropolis sampler transition rule.

The provided key is unique and does not need to be split.

It should return an immutable data structure.

Parameters:

  • sampler (MetropolisSampler) – The Metropolis sampler.

  • machine (Module) – A Flax module with the forward pass of the log-pdf.

  • params (Any) – The PyTree of parameters of the model.

  • key (Any) – A Jax PRNGKey.

Return type:

Any | None

Returns:

An optional state.

random_state(sampler, machine, params, sampler_state, key)[source]#

Generates a random state compatible with this rule.

By default this calls netket.hilbert.random.random_state().

Parameters:

  • sampler (MetropolisSampler) – The Metropolis sampler.

  • machine (Module) – A Flax module with the forward pass of the log-pdf.

  • params (Any) – The PyTree of parameters of the model.

  • sampler_state (SamplerState) – The current state of the sampler. Should not modify it.

  • key (Any) – The PRNGKey to use to generate the random state.

replace(**kwargs)[source]#

Replace the values of the fields of the object with the values of the keyword arguments. If the object is a dataclass, dataclasses.replace will be used. Otherwise, a new object will be created with the same type as the original object.

Return type:

TypeVar(P, bound= Pytree)

Parameters:

  • self (P)

  • kwargs (Any)

reset(sampler, machine, params, sampler_state)[source]#

Resets the internal state of the Metropolis Sampler Transition Rule.

The default implementation returns the current rule_state without modifying it.

Parameters:

  • sampler (MetropolisSampler) – The Metropolis sampler.

  • machine (Module) – A Flax module with the forward pass of the log-pdf.

  • params (Any) – The PyTree of parameters of the model.

  • sampler_state (SamplerState) – The current state of the sampler. Should not modify it.

Return type:

Any | None

Returns:

A reset state of the rule. This returns the same type of rule_state() and might be None.

transition(sampler, machine, parameters, state, key, σ)[source]#

Proposes a new configuration set of configurations $sigma’$ starting from the current chain configurations \(\sigma\).

The new configurations \(\sigma'\) should be a matrix with the same dimension as \(\sigma\).

This function should return a tuple. where the first element are the new configurations $sigma’$ and the second element is either None or an array of length σ.shape[0] containing an optional log-correction factor. The correction factor should be non-zero when the transition rule is non-symmetrical.

Parameters:

  • sampler – The Metropolis sampler.

  • machine – A Flax module with the forward pass of the log-pdf.

  • params – The PyTree of parameters of the model.

  • sampler_state – The current state of the sampler. Should not modify it.

  • key – A Jax PRNGKey to use to generate new random configurations.

  • σ – The current configurations stored in a 2D matrix.

Returns:

A tuple containing the new configurations \(\sigma'\) and the optional vector of log corrections to the transition probability.

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