The two-state Bose-Hubbard model in the hard-core boson limit: Non-ergodicity and the Bose-Einstein condensation

TL;DR

This paper investigates Bose-Einstein condensation in a two-state hard-core boson Bose-Hubbard model, highlighting the role of non-ergodic contributions and static density fluctuations near the superfluid phase transition.

Contribution

It introduces a detailed analysis of non-ergodicity effects in the HCB limit of the two-state Bose-Hubbard model using Green functions and spectral density calculations.

Findings

Non-ergodic contributions become significant near the superfluid phase transition.

Static density fluctuations are strongly enhanced close to the tricritical point.

Non-ergodic effects are comparable to ergodic ones in the superfluid phase.

Abstract

The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated. For the purpose of considering the non-ergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions. The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations) increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point.