Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines

TL;DR

This paper demonstrates that Restricted Boltzmann Machines can effectively learn and generate configurations of frustrated magnetic systems, capturing complex correlations and symmetry-breaking phenomena in various phases.

Contribution

It introduces RBMs as a versatile tool for modeling degenerate and constrained spin states in frustrated magnets, including complex phases like kagome spin ice.

Findings

RBMs accurately reproduce correlations in the 1D ANNNI model.

RBMs successfully learn local ice rules and correlations in kagome spin ice.

Proper bias fields are essential for modeling symmetry-broken phases.

Abstract

We show that Restricted Boltzmann Machines (RBMs) provide a flexible generative framework for modeling spin configurations in disordered yet strongly correlated phases of frustrated magnets. As a benchmark, we first demonstrate that an RBM can learn the zero-temperature ground-state manifold of the one-dimensional ANNNI model at its multiphase point, accurately reproducing its characteristic oscillatory and exponentially decaying correlations. We then apply RBMs to kagome spin ice and show that they successfully learn the local ice rules and short-range correlations of the extensively degenerate ice-I manifold. Correlation functions computed from RBM-generated configurations closely match those from direct Monte Carlo simulations. For the partially ordered ice-II phase -- featuring long-range charge order and broken time-reversal symmetry -- accurate modeling requires RBMs with uniform-sign bias fields, mirroring the underlying symmetry breaking. These results highlight the utility of RBMs as generative models for learning constrained and highly frustrated magnetic states.