Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas**Project supported by the National Natural Science Foundation of China (Grant Nos. 11374331 and 11534014) and the National Key R&D Program of China (Grant No. 2017YFA0304500). This work has been partially supported by CAS-TWAS President’s Fellowship for International PhD Students.

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 the two-point correlation function, the large moment tail of the momentum distribution, and the 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 terms of the fractional statistical parameter.