Quantum Group U_q(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain

TL;DR

This paper derives explicit formulas for one-point functions in the integrable spin-1 XXZ chain using symmetry relations and multiple integral evaluations, providing both analytical results and numerical validation.

Contribution

It introduces a method to explicitly evaluate one-point functions in the spin-1 XXZ chain by leveraging symmetry relations and gauge transformations.

Findings

Explicit integral formulas for spin-1 one-point functions

Numerical validation of analytical expressions

Symmetry relations among correlation functions

Abstract

We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.