How to control the initial sample

[miaoL1]

My lattice model is composed of two disconnected graphs, such as bi-layer graphene：

L = 1 #number of unit cells
graph = nk.graph.DoubledGraph(nk.graph.Honeycomb([L,L],pbc=True))
N = graph.n_nodes #number of sites
hi = nkx.hilbert.SpinOrbitalFermions(N, s=1/2, n_fermions=N)

I want to keep electron number in each layer conserved and fixed at half-filling.
this sampler

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

does help me keep electron number in each layer conversed, as the exchange only happens on points which are connected by edges in graph, and two layers are presented by disconnected graphs. However, the total charge difference, i.e. the electron number in each layer, is random and determined at the initial sample.

How can I guarantee that sampling only happens in subspace of half-filling in each layer?
I'd appreciate it if anyone can help.

[PhilipVinc]

I think it's documented in the doc of SpinOrbitalFermions.

I believe you just need to declare nkx.hilbert.SpinOrbitalFermions(N, s=1/2, n_fermions_per_spin=(N//2, N//2))

[miaoL1]

I see, the parameter "n_fermions_per_spin" keeps the spin conserved.
However, I want the sub-space which keeps the electron in two-layer half-filling.

[PhilipVinc]

hi = nkx.hilbert.SpinOrbitalFermions(N//2, s=1/2, n_fermions=N//2) * nkx.hilbert.SpinOrbitalFermions(N//2, s=1/2, n_fermions=N//2)

?

[miaoL1]

wow, I didn't expect to do this. Thanks!

[PhilipVinc]

Though this will change the encodings of the fermions, are the two spaces are concatenated. So you'll have
[layer 1 spin down..., layer 1 spin up..., layer 2 spin down..., layer 2 spin up...] instead of the current one you have which is
[layer 1 spin down, layer 2 spin down, layer 1 spin up, layer 2 spin up].

Also tensor Hilbert spaces don't probably play very well with Operators...

[PhilipVinc]

It might just be easier if you define a new ExchangeRule with a custom overriden init_state that does what you want.

[miaoL1]

by the way, I'm wondering what should I do if I both want the charge conservation in each two layer, and overall spin conservation(such as total spin = 0).