Reduction formula of form factors for the integrable spin-s XXZ chains and application to the correlation functions

TL;DR

This paper derives explicit formulas for spin-s form factors in the integrable XXZ chain, expressing them via scalar products of spin-1/2 operators, and applies these to compute correlation functions at zero temperature.

Contribution

It provides a detailed derivation of the fusion method for higher-spin XXZ form factors and revises previous results, enabling explicit correlation function calculations.

Findings

Explicit formulas for spin-s form factors in terms of spin-1/2 scalar products

Expression of correlation functions as sums of multiple integrals

Revised derivation of higher-spin XXZ form factors

Abstract

For the integrable spin-s XXZ chain we express explicitly any given spin-$s$ form factor in terms of a sum over the scalar products of the spin-1/2 operators. Here they are given by the operator-valued matrix elements of the monodromy matrix of the spin-1/2 XXZ spin chain. In the paper we call an arbitrary matrix element of a local operator between two Bethe eigenstates a form factor of the operator. We derive all important formulas of the fusion method in detail. We thus revise the derivation of the higher-spin XXZ form factors given in a previous paper. The revised method has several interesting applications in mathematical physics. For instance, we express the spin-$s$ XXZ correlation function of an arbitrary entry at zero temperature in terms of a sum of multiple integrals.