# High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain

## TL;DR

This paper investigates the high-temperature behavior of the transverse two-point correlation function in the XX quantum-spin chain using advanced mathematical techniques involving Riemann-Hilbert problems and Fredholm determinants.

## Contribution

It introduces a novel approach connecting the correlation function to a matrix Riemann-Hilbert problem and provides its asymptotic solution at high temperatures.

## Key findings

- Derived the leading high-temperature contribution to the correlation function.
- Connected the correlation function with a Riemann-Hilbert problem.
- Provided asymptotic analysis at fixed space-time separation.

## Abstract

We analyse the transverse dynamical two-point correlation function of the XX chain by means of a thermal form factor series. The series is rewritten in terms of the resolvent and the Fredholm determinant of an integrable integral operator. This connects it with a matrix Riemann-Hilbert problem. We express the correlation function in terms of the solution of the matrix Riemann-Hilbert problem. The matrix Riemann-Hilbert problem is then solved asymptotically in the high-temperature limit. This allows us to obtain the leading high-temperature contribution to the two-point correlation function at any fixed space-time separation.