Operator-valued Riemann-Hilbert problem for correlation functions of the XXZ spin chain

TL;DR

This paper formulates an operator-valued Riemann-Hilbert problem to analyze the correlation functions of the XXZ spin chain in the thermodynamic limit, providing a new mathematical framework for understanding these quantum systems.

Contribution

It introduces an operator-valued Riemann-Hilbert problem specifically for the XXZ spin chain's correlation functions, advancing the mathematical tools available for quantum integrable models.

Findings

Derived a system of integro-difference equations for the generating functional.

Established the operator-valued Riemann-Hilbert problem for the model.

Provides a foundation for future analytical solutions of correlation functions.

Abstract

The generating functional of correlation functions for the XXZ spin chain is considered in the thermodynamic limit. We derive a system of integro-difference equations that prescribe this functional. On the basis of this system we establish the operator-valued Riemann-Hilbert problem for correlation functions of the XXZ spin chain.