Bose-Einstein condensation and/or modulation of "displacements" in the two-state Bose-Hubbard model

TL;DR

This paper investigates phase transitions, including Bose-Einstein condensation and displacement modulation, in a two-state Bose-Hubbard model, analyzing conditions for various phases and their stability through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of instabilities and phase transitions in a two-state Bose-Hubbard model, including the conditions for SF and ordered phases, and discusses the absence of a supersolid phase.

Findings

SF phase can occur as an intermediate phase

Supersolid phase is thermodynamically unstable

Phase diagrams are calculated analytically and numerically

Abstract

Instabilities resulting in Bose-Einstein condensation and/or modulation of "displacements" in a system of quantum particles described by a two-state Bose-Hubbard model (with an allowance for the interaction between particle displacements on different lattice sites) are investigated. A possibility of modulation, which doubles the lattice constant, as well as the uniform displacement of particles from equilibrium positions are studied. Conditions for realization of the mentioned instabilities and phase transitions into the SF phase and into the "ordered" phase with frozen displacements are analyzed. The behaviour of order parameters is investigated and phase diagrams of the system are calculated both analytically (ground state) and numerically (at non-zero temperatures). It is revealed that the SF phase can appear as an intermediate one between the normal and "ordered" phases, while a supersolid phase is thermodynamically unstable and does not appear. The relation of the obtained results to the lattices with the double-well local potentials is discussed.