Green's Function Approach to the Bose-Hubbard Model

TL;DR

This paper introduces a Green's function approach using diagrammatic hopping expansion to analyze the Bose-Hubbard model, accurately predicting phase boundaries and excitation spectra at finite temperatures.

Contribution

It develops a non-perturbative Green's function method that improves upon mean-field results and aligns with Monte Carlo simulations for the Bose-Hubbard phase diagram.

Findings

Accurately predicts the superfluid-Mott insulator phase boundary.

Calculates excitation spectra and effective masses at finite temperature.

Shows second-order calculations improve phase boundary estimates.

Abstract

We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by the latest high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green's function approach allows for calculating the excitation spectrum at finite temperature and for determining the effective masses of particles and holes.