Finite-temperature dynamical structure factor of the Heisenberg-Ising chain

Abstract

We consider the spin-1/2 Heisenberg $XXZ$ chain in the regime of large Ising-type anisotropy $\ensuremath{\Delta}$. 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 $1/\ensuremath{\Delta}$ 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'').