Domain wall melting in spin-1 chains

TL;DR

This paper investigates the non-equilibrium spin dynamics in a non-integrable spin-1 XXZ chain, revealing three distinct phases and transient behaviors, with dynamics approximated by classical equations at large times.

Contribution

It introduces a novel simulation approach using TDVP for long-time dynamics in non-integrable spin chains, identifying phase-dependent behaviors and transient ballistic regimes.

Findings

Identifies diffusive, super-diffusive, and insulating phases based on anisotropy.

Discovers transient ballistic behavior with diverging crossover time near the isotropic point.

Shows that large-time dynamics align with classical Landau-Lifschitz equations.

Abstract

In this letter we study the non-equilibrium spin dynamics in the non-integrable spin-1 XXZ chain, emerging after joining two macroscopic pure states with different magnetizations. Employing the so-called time-dependent variational principle (TDVP) we simulate the dynamics of the total magnetization in the right (left) half of the system up to times that are normally inaccessible by standard tDMRG methods. We identify three distinct phases depending on the anisotropy of the chain, corresponding to diffusive, marginally super-diffusive and insulating. We observe a transient ballistic behaviour with a crossover time that diverges as the isotropic point is approached. We conclude that on intermediate-large time scales the dynamics is well described by the integrable Landau-Lifschitz classical differential equation.