An exact reformulation of the Bose-Hubbard model in terms of a stochastic Gutzwiller ansatz

TL;DR

This paper introduces an exact reformulation of the Bose-Hubbard model using a stochastic Gutzwiller ansatz, improving Monte Carlo simulations for strongly correlated bosonic phases like Mott insulators and Tonks gases.

Contribution

It extends previous stochastic Hartree methods to a Gutzwiller ansatz, enhancing computational efficiency for complex bosonic phases in the Bose-Hubbard model.

Findings

Demonstrated transition from Tonks gas to Mott phase in 1D lattice

Validated the stochastic method with numerical simulations

Improved simulation efficiency for strongly correlated phases

Abstract

We extend our exact reformulation of the bosonic many-body problem in terms of a stochastic Hartree ansatz to a stochastic Gutzwiller ansatz for the Bose Hubbard model. This makes the corresponding Monte Carlo method more efficient for strongly correlated bosonic phases like the Mott insulator phase or the Tonks phase. We present a first numerical application of this stochastic method to a system of impenetrable bosons on a 1D lattice showing the transition from the discrete Tonks gas to the Mott phase as the chemical potential is increased.