Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices

TL;DR

This paper provides an exact analysis of how finite temperature affects the properties of hard-core bosons in one-dimensional optical lattices, including correlations and momentum distributions, with comparisons between statistical ensembles.

Contribution

It introduces an exact method using Jordan-Wigner transformation to study finite-temperature effects on hard-core bosons in 1D lattices, including ensemble comparisons.

Findings

Minor differences between grand-canonical and canonical results for small systems.

Finite temperature significantly influences one-particle correlations and momentum distributions.

The method applies to systems with as few as 10 bosons in 50 sites.

Abstract

We present an exact study of the finite-temperature properties of hard-core bosons (HCB's) confined on one-dimensional optical lattices. Our solution of the HCB problem is based on the Jordan-Wigner transformation and properties of Slater determinants. We analyze the effects of the temperature on the behavior of the one-particle correlations, the momentum distribution function, and the lowest natural orbitals. In addition, we compare results obtained using the grand-canonical and canonical descriptions for systems like the ones recently achieved experimentally. We show that even for such small systems, as small as 10 HCB's in 50 lattice sites, there are only minor differences between the energies and momentum distributions obtained within both ensembles.