Finite Temperature Dynamical Structure Factor of the Heisenberg-Ising Chain

TL;DR

This paper develops a perturbative approach to analyze the finite-temperature dynamical structure factor of the Heisenberg XXZ chain with large anisotropy, revealing how spectral features evolve with temperature.

Contribution

It introduces a novel perturbative expansion in 1/Δ for the dynamical spin structure factor, unifying low-energy and zero-temperature behaviors in the large anisotropy regime.

Findings

Two-spinon continuum narrows with increasing temperature

Spectral weight shifts from two-spinon continuum to Villain mode

The approach captures temperature effects on dynamical response

Abstract

We consider the spin-1/2 Heisenberg XXZ chain in the regime of large Ising-like anisotropy $\Delta$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1\Delta$ for the transverse dynamical spin structure factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the T=0 two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (`Villain mode').