M. -S. Wang, J. -H. Huang, C. -H. Lee, X. -G. Yin, X. -W. Guan, M. T. Batchelor
The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for this model at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation $g^{(2)}(0)$ has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ at quantum criticality, where $n$ is the linear density and $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$. This suggests the possibility to test finite temperature local pair correlations for the TLL over the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation. The virial expansion is more suitable for the weak interaction regime.
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http://arxiv.org/abs/1211.3267
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