Degenerate approach to the mean field Bose- Hubbard Hamiltonian

TL;DR

This paper introduces a degenerate mean field perturbation method for the Bose-Hubbard model that avoids singularities at integer chemical potentials and accurately predicts phase boundaries.

Contribution

It presents a novel degenerate perturbation approach that improves the analysis of the Bose-Hubbard Hamiltonian near degeneracies.

Findings

The method yields finite second order ground state energies at degeneracies.

Phase boundary predictions match conventional mean field results.

The approach removes singularities present in traditional methods.

Abstract

A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction based on the conventional mean field perturbation approach.