One-body dynamical correlation function of the Lieb-Liniger model at finite temperature

The dynamical correlated properties of one-dimensional (1D) Bose gases provide profound understanding of novel physics emergent from collective excitations, for instance, the breakdown of off-diagonal long-range order, and the establishment of Tomonaga-Luttinger liquid theory. However, due to the nonperturbative nature of 1D many-body systems, the exact evaluation of correlation functions is notoriously difficult. Here, by means of a form factor approach based on an algebraic Bethe ansatz and numerics, we present a thorough study on the one-body dynamical correlation function (1BDCF) of the Lieb-Liniger model at finite temperature. The influence of thermal fluctuation and interaction on the behavior of 1BDCF has been demonstrated and analyzed from various perspectives, including the spectral distribution, the line shape at fixed momentum, and the corresponding static correlations.