English

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

Statistical Mechanics 2019-08-30 v2

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.

Keywords

Cite

@article{arxiv.1905.08756,
  title  = {Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point},
  author = {Grégoire Misguich and Nicolas Pavloff and Vincent Pasquier},
  journal= {arXiv preprint arXiv:1905.08756},
  year   = {2019}
}

Comments

45 pages, 21 figures. Submitted to SciPost. v2: Updated Fig. 11 (entanglement entropy) and various minor changes