MetropolisExchange

This sampler acts locally only on two local degree of freedom and , and proposes a new state: , where in general and . The sites and are also chosen to be within a maximum graph distance of .

The transition probability associated to this sampler can be decomposed into two steps:

  1. A pair of indices , and such that , is chosen with uniform probability.
  2. The sites are exchanged, i.e. and .

Notice that this sampling method generates random permutations of the quantum numbers, thus global quantities such as the sum of the local quantum n umbers are conserved during the sampling. This scheme should be used then only when sampling in a region where is needed, otherwise the sampling would be strongly not ergodic.

Class Constructor

Constructs a new MetropolisExchange sampler given a machine and a graph.

Argument Type Description
machine netket.machine.Machine A machine used for the sampling. The probability distribution being sampled from is .
graph netket.graph.Graph A graph used to define the distances among the degrees of freedom being sampled.
d_max int=1 The maximum graph distance allowed for exchanges.

Examples

Sampling from a RBM machine in a 1D lattice of spin 1/2, using nearest-neighbours exchanges.

>>> import netket as nk
>>>
>>> g=nk.graph.Hypercube(length=10,n_dim=2,pbc=True)
>>> hi=nk.hilbert.Spin(s=0.5,graph=g)
>>>
>>> # RBM Spin Machine
>>> ma = nk.machine.RbmSpin(alpha=1, hilbert=hi)
>>>
>>> # Construct a MetropolisExchange Sampler
>>> sa = nk.sampler.MetropolisExchange(machine=ma,graph=g,d_max=1)
>>> print(sa.hilbert.size)
100

Class Methods

reset

Resets the state of the sampler, including the acceptance rate statistics and optionally initializing at random the visible units being sampled.

Argument Type Description
init_random bool=False If True the quantum numbers (visible units)

seed

Seeds the random number generator used by the Sampler.

Argument Type Description
base_seed int The base seed for the random number generator

sweep

Performs a sampling sweep. Typically a single sweep consists of an extensive number of local moves.

Properties

Property Type Description
acceptance numpy.array The measured acceptance rate for the sampling. In the case of rejection-free sampling this is always equal to 1.
hilbert netket.hilbert The Hilbert space used for the sampling.
machine netket.machine The machine used for the sampling.
visible numpy.array The quantum numbers being sampled, and distributed according to