Correlation functions of the higher spin XXX chains

TL;DR

This paper develops a method using Algebraic Bethe Ansatz to compute correlation functions in higher spin XXX chains, extending techniques from spin 1/2 chains to arbitrary spins and deriving integral formulas in the thermodynamic limit.

Contribution

It introduces a new representation for correlation functions of higher spin chains and applies the quantum inverse problem approach to derive integral formulas for spin 1 in the thermodynamic limit.

Findings

Representation for finite chain correlation functions for arbitrary spin

Application of string solutions in the thermodynamic limit

Multiple integral formulas for spin 1 zero temperature correlations

Abstract

Using the Algebraic Bethe Ansatz we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero temperature correlation functions is obtained in the thermodynamic limit.