Phase diagram of the bose Hubbard model

TL;DR

This paper presents an analytic calculation of the phase diagram for the Bose-Hubbard model, accurately matching numerical results in one dimension and capturing key features in higher dimensions.

Contribution

It provides the first reliable analytic expressions for the phase diagram of the Bose-Hubbard model across different dimensions, including explicit energy formulas.

Findings

Excellent agreement with Monte Carlo results in 1D

Correct shape of Mott lobes in higher dimensions

Explicit strong-coupling energy expressions

Abstract

The first reliable analytic calculation of the phase diagram of the bose gas on a $d$-dimensional lattice with on-site repulsion is presented. In one dimension, the analytic calculation is in excellent agreement with the numerical Monte Carlo results. In higher dimensions, the deviations from the Monte Carlo calculations are larger, but the correct shape of the Mott insulator lobes is still obtained. Explicit expressions for the energy of the Mott and the ``defect'' phase are given in a strong-coupling expansion.