# Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

## TL;DR

This paper investigates the dynamics of a quantum spin chain with a domain wall, demonstrating that classical Landau-Lifshitz equations effectively describe its long-term behavior near the isotropic point, highlighting a semiclassical correspondence.

## Contribution

It provides a quantitative comparison between quantum dynamics and classical Landau-Lifshitz equations, showing their agreement near the isotropic point without adjustable parameters.

## Key findings

- Quantum and classical models agree in the long-time limit near the isotropic point.
- Energy conservation explains the quantum-classical correspondence.
- Variational solutions from the nonlinear Schrödinger equation capture key features.

## Abstract

We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.