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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
- Published as SciPost Phys. 7, 025 (2019)
|As Contributors:||Grégoire Misguich · Nicolas Pavloff|
|Arxiv Link:||https://arxiv.org/abs/1905.08756v2 (pdf)|
|Date submitted:||2019-07-29 02:00|
|Submitted by:||Misguich, Grégoire|
|Submitted to:||SciPost Physics|
|Subject area:||Condensed Matter Physics - Theory|
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.
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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
> (...) 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 ?
> 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
> 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
> 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.
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.
* 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
> (5) Typo later —> latter (appears many times in text)
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 3 on 2019-8-20 Invited Report
All my previous criticism has been addressed, the paper can be published now.
Anonymous Report 2 on 2019-7-31 Invited Report
The authors have successfully responded to the criticism and introduced the necessary charges in the manuscript. The paper is now suitable for publication.
Anonymous Report 1 on 2019-7-31 Invited Report
The authors have convincingly addressed all the issues in my previous report, the manuscript could be accepted as it is.