Real-time energy dynamics in spin-1/2 Heisenberg chains

TL;DR

This paper investigates the real-time energy transport in spin-1/2 Heisenberg chains, demonstrating ballistic energy propagation in different phases and connecting numerical results with Luttinger Liquid theory.

Contribution

It provides a detailed numerical and theoretical analysis of energy dynamics in the XXZ chain, highlighting ballistic behavior and wave-packet propagation with sound velocity.

Findings

Energy propagates ballistically in both phases.

Energy wave-packets travel at the sound velocity.

Numerical results agree with Luttinger Liquid predictions.

Abstract

We study the real-time dynamics of the local energy density in the spin-1/2 XXZ chain starting from initial states with an inhomogeneous profile of bond energies. Numerical simulations of the dynamics of the initial states are carried out using the adaptive time-dependent density matrix renormalization group method. We analyze the time dependence of the spatial variance associated with the local energy density to classify the dynamics as either ballistic or diffusive. Our results are consistent with ballistic behavior both in the massless and the massive phase. We also study the same problem within Luttinger Liquid theory and obtain that energy wave-packets propagate with the sound velocity. We recover this behavior in our numerical simulations in the limit of very weakly perturbed initial states.