Temperature-driven crossover in the Lieb-Liniger model

TL;DR

This paper studies how temperature affects the long-distance density correlations in the Lieb-Liniger model, revealing a temperature-induced crossover from non-oscillatory to oscillatory behavior across different interaction strengths.

Contribution

It provides a comprehensive numerical analysis of the finite-temperature correlation lengths in the Lieb-Liniger model, highlighting the temperature-driven crossover phenomena and their dependence on interaction strength.

Findings

Oscillatory behavior emerges at a critical temperature depending on interaction strength.

Complex asymptotic behavior with double crossover near the Tonks-Girardeau limit.

Crossovers occur only at intermediate coupling, not at zero or infinite interaction.

Abstract

The large-distance behavior of the density-density correlation function in the Lieb-Liniger model at finite temperature is investigated by means of the recently derived nonlinear integral equations characterizing the correlation lengths. We present extensive numerical results covering all the physical regimes fromweak to strong interaction and all temperatures. We find that the leading term of the asymptotic expansion becomes oscillatory at a critical temperature which decreases with the strength of the interaction. As we approach the Tonks-Girardeau limit the asymptotic behavior becomes more complex with a double crossover of the largest and next-largest correlation lengths. The crossovers exist only for intermediate couplings and vanish for $\gamma=0$ and $\gamma=\infty$.