Strong-coupling expansions for the pure and disordered bose Hubbard model

TL;DR

This paper develops a strong-coupling expansion method to accurately determine the phase boundary of the Bose-Hubbard model, including disordered systems, aligning well with Monte Carlo and exact results.

Contribution

It introduces a strong-coupling series expansion approach for both pure and disordered Bose-Hubbard models, capturing critical behaviors and disorder effects.

Findings

Series expansions match Monte Carlo accuracy

Disorder induces a first-order kink in the phase boundary

Critical behavior varies with dimensionality

Abstract

A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the bose Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide results that are as accurate as the Monte Carlo simulations and agree with the exact solutions. The shape difference between Kosterlitz-Thouless critical behavior in one-dimension and power-law singularities in higher dimensions arises naturally in this strong-coupling expansion. Bounded disorder distributions produce a ``first-order'' kink to the Mott phase boundary in the thermodynamic limit because of the presence of Lifshitz's rare regions.