A numerical exact solution of the Bose-Hubbard model

TL;DR

This paper presents a systematic strong-coupling expansion method to obtain numerically exact results for the Bose-Hubbard model in 1D and 2D, accurately determining phase diagrams and excitation spectra.

Contribution

It introduces a numerical approach that provides exact results for the structure factor and excitation spectrum, improving understanding of phase transitions in the Bose-Hubbard model.

Findings

Confirmed reentrance behavior near the critical point in 1D

Determined phase diagram and critical endpoints accurately

Provided exact excitation spectra for Mott insulator

Abstract

In this paper we report results from a systematic strong-coupling expansion of the Bose-Hubbard model in one and two spatial dimensions. We obtain numerically exact results for the structure factor and the spectrum of single particle and single hole excitations in the Mott insulator. This enables the determination of the zero-temperature phase diagram and the location of the critical endpoints of the Mott lobes. In one dimension we confirm the occurrence of reentrance behavior from the compressible to the insulating phase in a region close to the critical point.