Translational symmetry in RBM

[abukva]

Hi, I've encountered a bit of a simple problem, but it could also be that I misunderstood something. I am trying to simulate a simple 1D Transverse Ising at the critical point and I would like to run larger system sizes, like a couple of hundreds. My idea was that if I use RBMSymm with translational symmetry that would greatly simplify the problem and I could run larger systems. But when I do introduce symmetries there isn't any noticeable difference in the run time or convergence speed. Am I missing something?

Simple code I am running:

N = 20
g = nk.graph.Hypercube(length=N, n_dim=1, pbc=True)
hi = nk.hilbert.Spin(s=1/2, N=g.n_nodes)
H = nk.operator.Ising(hilbert=hi, h = 1, J=-1, graph = g)
ma = nk.models.RBMSymm(g.translation_group(), alpha=1.)
sa = nk.sampler.MetropolisLocal(hilbert=hi, n_chains=32)
op = nk.optimizer.Sgd(learning_rate=0.05)
sr = nk.optimizer.SR(diag_shift=0.1)
vs = nk.vqs.MCState(sa, ma, n_samples=4800)
gs = nk.VMC(hamiltonian=H, optimizer=op, preconditioner=sr,  variational_state=vs)
gs.run(out=None, n_iter=400)

[PhilipVinc]

Hi @abukva ,

My idea was that if I use RBMSymm with translational symmetry that would greatly simplify the problem

Depends what you mean by Simplifying the problem. You still are trying to solve a quantum mechanic hamiltonian with exponentially many degrees of freedom 2^N, and you are removing a number of N degrees of freedom, so that's really little.

Mainly, you are constraining the NQS to be symmetric, and you know the ground state is symmetric, which can speed up convergence and/or yield better results.

and I could run larger systems

Not really. Computational and memory cost will be comparable. Mainly you get better results.

there isn't any noticeable difference in the run time or convergence speed

Runtime, you should not expect speedups.
Convergence speed, it's problem-dependent. It really depends on the optimiser and learning rate.
On such a simple problem like 1D Ising.

In short: Symmetries lead to better (more accurate) results, but they don't, in general, speedup calculations or convergence.