A self-consistent Hartree-Fock approach for interacting bosons in optical lattices

TL;DR

This paper introduces a self-consistent Hartree-Fock method for interacting bosons in optical lattices, starting from exact single-particle states, providing insights beyond the tight-binding approximation especially at high fillings.

Contribution

It presents a novel approach using exact single-particle states and a self-consistent Hartree-Fock approximation for better modeling of interacting bosons in optical lattices.

Findings

Predictions for superfluid transition temperature

Calculations of condensate fraction

Analysis of boson momentum distribution

Abstract

A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.