Title Universal local pair correlations of Lieb-Liniger bosons at

Ming‐Ming Wang, J.-H. Huang, Chaohong Lee +3 more

Guillaume Lang

Jean-Sébastien Caux, Pasquale Calabrese

Vladimir Lvovich Lyuboshitz, M.I. Podgoretsky

Ming‐Ming Wang, Jiahao Huang, Chaohong Lee +3 more

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 ${g}^{(2)}(0)\ensuremath{\approx}2p/(n\ensuremath{\varepsilon})$ 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 $\ensuremath{\varepsilon}=\frac{{\ensuremath{\hbar}}^{2}}{2m}{c}^{2}$ 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.

Vadim Cheianov, H. Smith, Mikhail B. Zvonarev

We develop a method to calculate vacuum expectation values of local operators in the Lieb–Liniger model. This method is based on a set of new identities obtained using integrability and effective theory ('bosonization') description. We use this method to get an explicit expression for the three-body local correlation function, measured in a recent experiment.