How to Modify Exchange Rules in Metropolis Sampling for 1/2 Spin Fermion Systems in NetKet?

[Mio826]

(This is a question due to lack of experience)
When doing Metropolis sampling on a 1/2 spin fermion system, the exchange rule seems to only allow exchange of electrons within a total spin conserved subspace according to this file: netket\sampler\rules\exchange.py
.
If I faile to understand the code right, please advise me, otherwise, how should I change this rule, to allow exchange of electrons with different spin? (besides inputing another clusters or graph including two subspace)

[PhilipVinc]

See https://netket.readthedocs.io/en/latest/api/_generated/samplers/netket.sampler.MetropolisExchange.html#netket.sampler.MetropolisExchange

If you are working with systems where the number of nodes in the physical lattice does not match the number of degrees of freedom, you must be careful!

A typical example is a system of Spin-1/2 fermions on a lattice with N sites, where the first N degrees of freedom correspond to the spin down degrees of freedom and the next N degrees of freedom correspond to the spin up degrees of freedom.

In this case, you tipically want to exchange only degrees of freedom of the same type. A simple way to achieve this is to double the graph:

import netket as nk
g = nk.graph.Square(5)
hi = nkx.hilbert.SpinOrbitalFermions(g.n_nodes, s=0.5)

exchange_graph = nk.graph.disjoint_union(g, g)
print("Exchange graph size:", exchange_graph.n_nodes)

sa = nk.sampler.MetropolisExchange(hi, graph=exchange_graph, d_max=1)