Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

Abstract

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M -particle correlation functions, momentum distribution and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate twopoint correlation function, the large moment tail of momentum distribution and static structure factor of the model in terms of the fractional statistical parameter α = 1 − 2/γ, where γ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in term of the fractional statistical parameter.

Correlation in Momentum Space of Tonks-Girardeau Gas

“…Tonks-Gigrardeau (TG) gas [21,22] is a strong-correlation system, which is the 1D ultracold bosonic atom gases with infinite repulsive interaction. The one-body, two-body * Electronic address: haoyj@ustb.edu.cn and three-body correlation functions [23,24], static and dynamical structure factor [25,26], and universal contact of the system has been studied [27]. So far, most related study are done in coordinate space.…”