Correlation functions of the Lieb-Liniger gas and the LeClair-Mussardo formula

TL;DR

This paper derives multi-point correlation functions for the Lieb-Liniger gas in various states using a series of multiple integrals, confirming the LeClair-Mussardo formula for relativistic models.

Contribution

It provides a new derivation of correlation functions for the Lieb-Liniger gas that aligns with the LeClair-Mussardo formula, extending its applicability.

Findings

Correlation functions expressed as multiple integrals

Rapid convergence for short distances and low densities

Exact match with LeClair-Mussardo formula

Abstract

In this letter we derive formulas for multi point correlation functions, in the thermodynamic limit, for the Lieb Liniger gas taken with respect to arbitrary eigenstates. These results apply for the ground state, thermal states and GGE states. We obtain these correlation functions as a series of multiple integrals of progressively higher dimensions. These integrals converge rapidly for short distance correlation functions and low densities of particles. The series derived matches exactly the LeClair Mussardo formula for correlation functions of relativistic integrable models.