Finite-temperature quantum rotor approach for ultracold bosons in optical lattices

TL;DR

This paper develops a finite-temperature extension of the quantum-rotor approach to accurately describe ultracold bosons in optical lattices at non-zero temperatures, aligning well with experimental observations.

Contribution

It introduces a resummation and auxiliary-variable expansion to extend QRA to finite temperatures, maintaining analytical power and flexibility.

Findings

Accurately models the shrinkage of Mott lobes up to T/U ≈ 0.2

Quantitative agreement with theoretical predictions and experiments

Provides a computationally light analytic tool for strongly correlated bosons

Abstract

Interacting bosons in optical lattices directly expose quantum phases in a clean, highly controllable environment. This requires engineering systems with very low entropies, but the resulting temperature--interaction ratios $T/U$ of present experiments remain well above the domain where zero-temperature theories are expected to be reliable. The quantum-rotor approach (QRA), while analytically powerful and extremely flexible, inherits ground-state phase correlations and therefore breaks down once thermal winding of the phase field becomes significant. Here we construct a finite-temperature extension of QRA by (i) performing resummation of winding-number contributions for temperatures $k_{B}T/U\lesssim 0.2$ and (ii) developing an auxiliary-variable expansion that remains accurate toward the classical limit. The resulting closed expression for the phase correlator is inserted into the standard spherical-approximation QRA without sacrificing the method's flexibility with respect to lattice geometry and dimensionality. The approach reproduces the shrinkage of Mott lobes from $T=0$ up to $k_{B}T/U\simeq 0.2$ in quantitative agreement with theoretical predictions and with in-situ imaging experiments. This finite-T QRA thus supplies an analytic, computationally light tool for strongly correlated lattice bosons and sets the stage for amplitude-fluctuation upgrades required at higher temperatures.