Bose-Einstein condensation in tight-binding bands

TL;DR

This paper provides a comprehensive theoretical analysis of Bose-Einstein condensation across different lattice structures, examining effects of interactions and filling, and identifying conditions for highest condensation temperature and localization.

Contribution

It introduces a unified theoretical framework for studying boson condensation in various lattice geometries, including weak and strong interactions, and explores the transition to a Mott insulator.

Findings

Bcc lattice yields highest Bose condensation temperature.

Interaction effects can both deplete and enhance condensate fraction.

Strong interactions lead to localization and Mott insulator formation.

Abstract

We present a theoretical study of condensation of bosons in tight binding bands corresponding to simple cubic, body centered cubic, and face centered cubic lattices. We have analyzed non-interacting bosons, weakly interacting bosons using Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body centered cubic lattice has the highest Bose condensation temperature. The growth of condensate fraction of non-interacting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes them to form a Bose-Mott-Hubbard insulator for integer filling.