Off-diagonal long-range order in a harmonically confined two-dimensional Bose gas

TL;DR

This paper explores off-diagonal long-range order in a 2D harmonically confined Bose gas, revealing a possible reentrant order phase related to a transition distinct from Bose-Einstein condensation.

Contribution

It provides an analytical description of spatial correlations in a 2D Bose gas, including effects of interactions, and identifies a reentrant order phase separate from BEC.

Findings

Exact finite-temperature correlation description in noninteracting case

Reentrant off-diagonal long-range order below a certain temperature

Order revival linked to a phase transition distinct from BEC

Abstract

We investigate the presence of off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. In the noninteracting case, an analytical calculation of the the finite-temperature one-particle density martix provides an exact description of the spatial correlations known to be associated with the existence of a Bose-Einstein condensate below the transition temperature $T^{(0)}_c$. We treat the effects of repulsive interactions within the semiclassical Hartree-Fock-Bogliubov approximation and find that even though the system remains in the same {\em uncondensed phase} for all $T \geq 0$, there appears to be a revival of off-diagonal long-range order for temperatures $T < T^{(0)}_c$. We suggest that this reentrant order is related to a phase transition in the system which {\em is not} the BEC state.