Leggett's bound and superfluidity in strongly interacting bosons

TL;DR

This paper assesses the effectiveness of Leggett's superfluid bound in strongly interacting bosonic systems, demonstrating its reliability in certain regimes and identifying conditions where it fails, through advanced computational methods.

Contribution

It extends the understanding of Leggett's bound beyond mean-field regimes by testing its accuracy in strongly interacting 2D-1D bosonic systems using quantum Monte Carlo and other methods.

Findings

Leggett's bound reliably estimates superfluid fraction in strongly interacting regimes at low temperatures.

The bound fails to predict superfluidity in certain counterexamples, indicating limitations.

The study clarifies the conditions under which Leggett's bound is a good predictor.

Abstract

A density-based superfluid bound called Leggett's bound has been proved to be a good estimator of the superfluid fraction for cold atomic gases in the mean-field regime. Here, we investigate the accuracy of such bound in the strongly interacting regime, where the mean-field approach fails. Combining quantum Monte Carlo, Gross-Pitaevskii equation and field-theory calculations, we demonstrate that the bound serves as a reliable estimator of the superfluid fraction for strongly interacting bosons at 2D-1D dimensional crossover at low temperatures. By further presenting two counterexamples where the bound predicts trivial results, we shed light on the conditions under which the Leggett's bound serves as a good predictor.