# Ground state phase diagram of the one-dimensional Bose-Hubbard model from restricted Boltzmann machines

## TL;DR

This paper demonstrates that restricted Boltzmann machines can effectively model the ground state phase diagram of the one-dimensional Bose-Hubbard model, capturing phase boundaries between Mott insulator and superfluid phases.

## Contribution

It introduces a novel application of restricted Boltzmann machines to bosonic lattice models using NetKet, expanding their applicability in quantum many-body physics.

## Key findings

- Successfully mapped the phase diagram using RBMs
- Results agree qualitatively with exact diagonalization
- Identified phase boundaries between Mott insulator and superfluid phases

## Abstract

Motivated by recent advances in the representation of ground state wavefunctions of quantum many-body systems using restricted Boltzmann machines as variational ansatz, we utilize an open-source platform for constructing such ansatz called NetKet to explore the extent of applicability of restricted Boltzmann machines to bosonic lattice models. Within NetKet, we design and train these machines for the one-dimensional Bose-Hubbard model through a Monte Carlo sampling of the Fock space. We vary parameters such as the strength of the onsite repulsion, the chemical potential, the system size and the maximum site occupancy and use converged equations of state to identify phase boundaries between the Mott insulating and superfluid phases. We compare the average density and the energy to results from exact diagonalization and map out the ground state phase diagram, which agrees qualitatively with previous finding obtained through conventional means.