Dynamical correlation functions of the XXZ model at finite temperature

TL;DR

This paper derives a multiple integral representation for the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and magnetic field, unifying several known limits.

Contribution

It introduces a novel integral formula for dynamical correlations in the XXZ model at finite temperature, combining lattice path integrals with quantum inverse scattering.

Findings

Reproduces static, zero-temperature, and XY limits

Provides a unified framework for finite-temperature correlations

Enhances understanding of dynamical properties in quantum spin chains

Abstract

Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the following three limits: the static, the zero-temperature and the XY limits.