Discrete Symmetries and S Matrix of the XXZ Chain

TL;DR

This paper explores discrete symmetries in the XXZ spin chain, providing new insights into eigenvalues, state classification, and S matrix computation within the Quantum Inverse Scattering framework.

Contribution

It introduces a formal definition of parity, proposes eigenvalues for charge conjugation, and uses these symmetries to classify states and compute the S matrix.

Findings

Defined parity for the XXZ chain

Derived eigenvalues for charge conjugation

Computed the S matrix explicitly

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.