Accurate neural quantum states for interacting lattice bosons

TL;DR

This paper introduces a neural backflow Jastrow Ansatz that accurately models the ground state of 2D interacting lattice bosons, enabling large-scale simulations and analysis of quantum phase transitions.

Contribution

The authors develop a novel neural quantum state approach that achieves high accuracy for the 2D Bose-Hubbard model across all interaction strengths, surpassing previous methods.

Findings

Achieved state-of-the-art variational energies for 20x20 lattices.

Successfully modeled the ground state across all interaction regimes.

Enabled analysis of entanglement entropy scaling at the phase transition.

Abstract

In recent years, neural quantum states have emerged as a powerful variational approach, achieving state-of-the-art accuracy when representing the ground-state wave function of a great variety of quantum many-body systems, including spin lattices, interacting fermions or continuous-variable systems. However, accurate neural representations of the ground state of interacting bosons on a lattice have remained elusive. We introduce a neural backflow Jastrow Ansatz, in which occupation factors are dressed with translationally equivariant many-body features generated by a deep neural network. We show that this neural quantum state is able to faithfully represent the ground state of the 2D Bose-Hubbard Hamiltonian across all values of the interaction strength. We scale our simulations to lattices of dimension up to $20{\times}20$ while achieving the best variational energies reported for this model. This enables us to investigate the scaling of the entanglement entropy across the superfluid-to-Mott quantum phase transition, a quantity hard to extract with non-variational approaches.