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Journal Articles SciPost Physics Year : 2019

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

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.

Dates and versions

hal-02295825 , version 1 (24-09-2019)

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Cite

Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier. Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point. SciPost Physics, 2019, 7 (2), ⟨10.21468/SciPostPhys.7.2.025⟩. ⟨hal-02295825⟩
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