Universal local pair correlations of Lieb-Liniger bosons at quantum criticality
Yin, X. G.
Guan, X. W.
Batchelor, M. T.
Date of Issue2013
School of Materials Science and Engineering
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 the strong-coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value g(2)(0)≈2p/(nɛ) in the quantum critical regime, the TLL phase, and the quasiclassical region, where p is the pressure per unit length rescaled by the interaction energy ɛ=ℏ2/2mc2 with interaction strength c and linear density n. This suggests the possibility to test finite temperature local pair correlations for the TLL in 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.
Physical review A
© 2013 American Physical Society. This paper was published in Physical review A and is made available as an electronic reprint (preprint) with permission of American Physical Society. The paper can be found at the following official DOI: [http://dx.doi.org/10.1103/PhysRevA.87.043634]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.