The LeClair-Mussardo series and nested Bethe Ansatz

TL;DR

This paper generalizes the LeClair-Mussardo series to nested Bethe Ansatz systems, providing a new expansion theorem for correlation functions in integrable models with algebra symmetries, applicable to one- and two-point functions.

Contribution

It introduces an expansion theorem that extends the LeClair-Mussardo series to nested Bethe Ansatz models, enabling explicit correlation function calculations.

Findings

Derived an infinite integral series for correlation functions in nested Bethe Ansatz models.

Applied the series to the Gaudin-Yang model's density-density correlator in specific limits.

Provided explicit formulas in large coupling and imbalance regimes.

Abstract

We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(3)$. Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.