Form factors of bound states in the XXZ chain

TL;DR

This paper rigorously analyzes the large-volume behavior of form factors in the XXZ spin chain, focusing on bound states, and lays groundwork for understanding the asymptotic behavior of two-point functions.

Contribution

It provides a rigorous analysis of form factors involving bound states in the XXZ chain, based on properties of Bethe string solutions and technical hypotheses.

Findings

Derived large-volume asymptotics for form factors involving bound states.

Established conditions under which the analysis applies to generic excited states.

Paved the way for extracting large-distance and long-time asymptotics of two-point functions.

Abstract

This work focuses on the calculation of the large-volume behaviour of form factors of local operators in the XXZ spin-$1/2$ chain taken between the ground state and an excited state containing bound states. The analysis is rigorous and builds on various fine properties of the string solutions to the Bethe equations and certain technical hypotheses. These technical hypotheses are satisfied for a generic excited state. The results obtained in this work pave the way for extracting, starting from the first principles, the large-distance and long-time asymptotic behaviour of the XXZ chain's two-point functions just as the so-called edge singularities of their Fourier transforms.