Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain

TL;DR

This paper explores the parity and charge conjugation symmetries of the XXZ spin chain, providing a classification of states and a direct calculation of the S matrix within the Quantum Inverse Scattering framework.

Contribution

It introduces a formulation of parity and charge conjugation symmetries for the XXZ chain and computes the S matrix using these symmetries.

Findings

Classification of low-lying states using discrete symmetries

Explicit expression for charge conjugation eigenvalues

Direct computation of the S matrix

Abstract

We formulate the notion of parity for the periodic XXZ spin chain within the Quantum Inverse Scattering Method. We also propose an expression for the eigenvalues of the charge conjugation operator. We use these discrete symmetries to help classify low-lying S^z=0 states in the critical regime, and we give a direct computation of the S matrix.