Dynamics and Thermodynamics of the Bose-Hubbard model

TL;DR

This paper presents a systematic strong-coupling expansion of the Bose-Hubbard model in 1D and 2D, providing precise phase boundary and excitation data, and revealing reentrant behavior near the critical point.

Contribution

It offers the first numerically exact results for excitation dispersion and phase boundaries in the Bose-Hubbard model in low dimensions, serving as a benchmark for future numerical methods.

Findings

Exact dispersion of excitations in Mott insulator

Precise determination of Mott phase boundary

Observation of reentrant phase transition near critical point

Abstract

We report results from a systematic analytic strong-coupling expansion of the Bose-Hubbard model in one and two spatial dimensions. We obtain numerically exact results for the dispersion of single particle and single hole excitations in the Mott insulator. The boundary of the Mott phase can be determined with previously unattainable accuracy in one and two dimensions. In one dimension we observe the occurrence of reentrant behavior from the compressible to the insulating phase in a region close to the critical point which was conjectured in earlier work. Our calculation can be used as a benchmark for the development of new numerical techniques for strongly correlated systems.