The interaction energy of the particle-hole pair in the XXZ-spin chain

TL;DR

This paper calculates the interaction energy between particle-hole pairs in the XXZ-spin chain and links it to scattering phase shifts, aiding the understanding of threshold singularities in correlators.

Contribution

It provides a direct calculation of the particle-hole interaction energy and connects it to scattering phase shifts, offering new insights into the XXZ-spin chain.

Findings

Interaction energy expressed via scattering phase shifts

Connection to threshold singularities in correlators

Potential applications in calculating critical exponents

Abstract

We calculate directly the interaction energy of the eigenstate with the single particle and the single hole for the XXZ-spin chain. We find the connection of this addition to the energy with the two-particle forward scattering phase shift function. The results can have applications to the calculation of the exponents of the threshold singularities in the correlators of the XXZ-spin chain.