Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

TL;DR

This paper introduces an algebraic Bethe ansatz method to derive the long-distance asymptotics of correlation functions in integrable models, confirming predictions from Luttinger liquid and conformal field theories.

Contribution

It presents a first-principles approach to compute asymptotic correlation functions for integrable models, applicable to the XXZ Heisenberg chain and 1D Bose gas.

Findings

Confirmed Luttinger liquid predictions for the XXZ chain

Validated conformal field theory results for the Bose gas

Provided a systematic derivation of asymptotics from integrability

Abstract

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin correlation function of the XXZ Heisenberg spin-1/2 chain (with magnetic field) in the disordered regime as well as to the density-density correlation func- tion of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.