# Equilibrium dynamics of the XX chain

## TL;DR

This paper re-examines the equilibrium dynamics of the spin-1/2 XX chain using a new formalism, providing high-accuracy calculations of correlation functions and comparing them with existing theoretical and numerical results.

## Contribution

It introduces a formalism based on quantum transfer matrix and thermal form factors to evaluate real-time space correlation functions in the XX chain.

## Key findings

- Reproduces exact results in limiting cases
- Matches asymptotic formulas from Riemann-Hilbert approach
- Shows consistency with numerical Pfaffian evaluations and Luttinger liquid theory

## Abstract

The equilibrium dynamics of the spin-1/2 XX chain is re-examined within a recently developed formalism based on the quantum transfer matrix and a thermal form factor expansion. The transversal correlation function is evaluated in real time and space. The high-accuracy calculation reproduces several exact results in limiting cases as well as the well-known asymptotic formulas obtained by the matrix Riemann-Hilbert approach. Furthermore, comparisons to numerical data based on a direct evaluation of the Pfaffian as well as to asymptotic formulas obtained within non-linear Luttinger liquid theory are presented.