Temperature-driven crossover in the Lieb-Liniger model

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 $\gamma =\infty$.

5 pages, 4 figures, RevTeX 4.1

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• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Dynamical correlation functions in the Ising field theory