Solving the Bose-Hubbard model with machine learning

TL;DR

This paper introduces a neural network-based method to compute the ground state of the Bose-Hubbard model, showing promising results for quantum many-body problems in ultracold atoms.

Contribution

It proposes a neural network approach for the Bose-Hubbard model, demonstrating accuracy comparable to exact methods and Gutzwiller approximation.

Findings

Results agree well with exact diagonalization

Method outperforms Gutzwiller approximation in accuracy

Neural network approach is promising for quantum many-body problems

Abstract

Motivated by the recent successful application of artificial neural networks to quantum many-body problems [G. Carleo and M. Troyer, Science {\bf 355}, 602 (2017)], a method to calculate the ground state of the Bose-Hubbard model using a feedforward neural network is proposed. The results are in good agreement with those obtained by exact diagonalization and the Gutzwiller approximation. The method of neural-network quantum states is promising for solving quantum many-body problems of ultracold atoms in optical lattices.