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

by Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier

Submission summary

As Contributors: Grégoire Misguich · Nicolas Pavloff
Arxiv Link: https://arxiv.org/abs/1905.08756v2 (pdf)
Date accepted: 2019-08-22
Date submitted: 2019-07-29 02:00
Submitted by: Misguich, Grégoire
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Condensed Matter Physics - Theory
Approaches: Theoretical, Computational

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.

Ontology / Topics

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Density matrix renormalization group (DMRG) Domain walls Schrödinger equation XXZ model

Published as SciPost Phys. 7, 025 (2019)



Author comments upon resubmission

List of changes

=============
From "Report 1"
=============

> I do not think it is legitimate to proclaim
this derivation as "alternative" or "more direct"...

* The formulation has been changed in the revised version.

* We have improved the readability of the left panel of Fig. 9 (by a
better choice of colors, and by plotting the Landau-Lifshitz data
using crosses instead of a full line).

> Minor remarks: Bad spelling: "insure" should be "ensure" (end of
page 23). Just a suggestion which may slightly improve readability:
one could try use explicit symbols to the terms of the sort 1/4−S⋅S
and 1/4−Sz⋅Sz, e.g. using Hiso and V

* Done.

> (...) Saying "was observed to freeze" may read as an understatement.

* We agree with the referee (and changed the text accordingly).

=============
From "Report 2"
=============

> (...) Wouldn't it be more correct to say that there is no
exponential decay in the quantum case, since e−1=cst ?

* Corrected.

> 5) Page 21, caption to figure 11. 't=185' contradicts the claim
't=210' at the end of page 19. Also, inconsistent notations τ vs dt.

* Corrected (we updated this plot, now the entropy data are available up
to t=400)

> 7) Section 7.6, last paragraph. Perhaps it would be better to state
more clearly that the divergences are precisely the logarithmic
divergences that make up for the logarithmically enhanced diffusion
discussed before.

* Done.

> Typos:
> Page 2, 'form' -> 'from'.
> Page 4, line 12. 'and in characterize'.
> Page 4, the last sentence of the introduction starts with 'And'.
> Page 10, last line: 'r/r' ->'r/t'.
> Page 18, second paragraph in 7.1. 'As can be seen in in' -> 'As can be seen in'
> Page 26, line before equation (39). 'the following the filament' ->'the following filament'.
> Also, the filament function is 'ψ(x,t)' not u(x,t), so the sentence reads awkwardly.
> Page 26, two equations are not numbered.

Corrected, thanks.

============
From Report 3
============

* We have improved the discussion on the entropy, at the end of Sec. 7.2.
We have explained why the semi-classical entropy argument does not
apply away from Δ=1.

> The smaller corrections:
>
> (1) In Fig. 4 the labels (1) and (2) should
> be shifted in order not to overlap with the x axis. There is also an
> extra parenthesis in the y axis label of (2).
> (2) In Fig. 7, there is a typo in the legend, Ωx should read Ωz.

* Done

* Improved Fig. 8, to make visible the fact that the current vanishes at t=0.

> (4) Before Eq. (39): “filament function” ψ(r,t) I guess this should
read u(r,t).
> (5) Typo later —> latter (appears many times in text)

Corrected


Reports on this Submission

Anonymous Report 3 on 2019-8-20 Invited Report

Report

All my previous criticism has been addressed, the paper can be published now.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 2 on 2019-7-31 Invited Report

Report

The authors have successfully responded to the criticism and introduced the necessary charges in the manuscript. The paper is now suitable for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2019-7-31 Invited Report

Report

The authors have convincingly addressed all the issues in my previous report, the manuscript could be accepted as it is.

  • validity: high
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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