Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state

TL;DR

This paper investigates the long-time magnetization dynamics of a spin-1/2 Heisenberg chain from a domain-wall initial state, finding evidence for diffusive behavior and analyzing entanglement entropy evolution.

Contribution

The study provides extensive numerical evidence supporting diffusive magnetization dynamics in the Heisenberg chain from a domain-wall initial condition, including analysis of subleading corrections.

Findings

Magnetization profile exhibits diffusive behavior at long times

Subleading corrections decay slowly, affecting the emergence of diffusion

Entanglement entropy evolution is discussed

Abstract

We study the dynamics of an isotropic spin-1/2 Heisenberg chain starting in a domain-wall initial condition, where the spins are initially up on the left half-line and down on the right half-line. We focus on the long-time behavior of the magnetization profile. We perform extensive time-dependent density-matrix renormalization group simulations (up to t=350) and find that the data are compatible with a diffusive behavior. Subleading corrections decay slowly blurring the emergence of the diffusive behavior. We also compare our results with two alternative scenarios: superdiffusive behavior and enhanced diffusion with a logarithmic correction. We finally discuss the evolution of the entanglement entropy.