Benchmarking a restricted Boltzmann machine on the $\mathbb{Z}_2$ Bose-Hubbard chain in the adiabatic hard-core regime

TL;DR

This paper demonstrates that a shallow restricted Boltzmann machine can effectively model the ground state phase diagram of the one-dimensional $ obreak{Z}_2$ Bose-Hubbard chain in the adiabatic hard-core regime, capturing key phase features.

Contribution

It shows that a shallow RBM can reproduce the main adiabatic phase structure and symmetry-broken configurations of the $ obreak{Z}_2$ Bose-Hubbard chain at half filling.

Findings

Reproduces the overall phase diagram structure.

Distinguishes polarized and Néel-ordered regions.

Captures representative spin patterns and site occupations.

Abstract

We study the ground state of the $\mathbb{Z}_2$ Bose-Hubbard chain in the adiabatic hard-core limit at half filling using variational Monte Carlo with a shallow restricted Boltzmann machine as the variational ansatz. In this context, the neural quantum state is compared with the established adiabatic description of the model. The variational results reproduce the overall structure of the phase diagram obtained from magnetization observables, distinguish the polarized and N\'eel-ordered regions, and capture representative spin patterns and site occupations for the staggered insulating configurations selected by a weak symmetry-breaking field. Taken together, these results show that a shallow restricted Boltzmann machine reproduces the main adiabatic phase structure of the one-dimensional $\mathbb{Z}_2$ Bose-Hubbard chain and captures the selected symmetry-broken insulating configurations at half filling.