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 two-point correlation function, the large moment tail of momentum distribution and static structure factor of the model in terms of the fractional statistical parameter $\alpha =1-2/\gamma$, where $\gamma$ 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.

17 pages, various methods for calculating high order correlation functions of the Lieb-Liniger model

References in corpus (18)

• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Dynamical density-density correlations in the one-dimensional Bose gas
• Number of closed-channel molecules in the BEC-BCS crossover
• Universal Properties of the Ultra-Cold Fermi Gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Observation of Quantum Criticality and Luttinger Liquid in One-dimensional Bose Gases
• Momentum Distribution and Contact of the Unitary Fermi gas
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Universal One-dimensional Atomic Gases Near Odd-wave Resonance
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Universal Tan relations for quantum gases in one dimension
• Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions
• A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model
• Analytic solutions of the 1D finite coupling delta function Bose gas
• Critical phenomena in one dimension from a Bethe ansatz perspective

Cited by in corpus (1)

• $n$-body Correlation of Tonks-Girardeau Gas