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Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

by Sibaram Ruidas, Sumilan Banerjee

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Submission summary

Authors (as registered SciPost users): Sumilan Banerjee
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-10-15
Date submitted: 2021-10-02 04:59
Submitted by: Banerjee, Sumilan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatio-temporal chaotic properties have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusions, respectively. Our results also provide new insights into the dynamics of interacting quantum systems in the semiclassical limit.

Author comments upon resubmission

We have revised our manuscript following your comments. We are appending our responses to Anonymous Report 1 and your comments below.

  1. Response to Anonymous Report 1

Comment 1: The authors have responded to all the questions raised in my report dili- gently and made the requisite changes. I recommend the article for publication. We thank the referee for useful comments and for going through our manuscript again.

Response: We thank the referee for recommending publication.

Comment 2: A minor point - some references are not up to date - it will be good to review the references and make sure that the latest references are used. One that I noticed was Ref 42 which is now published in Phys Rev B ( 10.1103/Phys- RevB.102.184303).

Response: We have updated the above reference and other references with the citations to the latest published articles.

B. Response to Editor’s comment

Email Comment on 2021-7-28

We thank the editor for the important and useful comments. We have made modifications to the draft in response to the editor’s comments.

Comment 1: First, I think it would benefit from a pure English edit to break apart sentences with multiple subclauses, i.e. for examples. They make the introductory text very hard to parse.

Response: We have revised the introductory part following the above suggestion.

Comment 2: Second, I am somewhat confused about your use of the language of diffusion. The relevant conserved quantity is S z – yet in this manuscript you refer to C xy (t) ∼ 1/t a with small a in the KT phase as ‘sub-diffusion’. My understanding is that, if anything, the KT phase should exhibit superflow of S z , just like a U (1) breaking superfluid has j = ∇φ s super flow of n in parallel with a normal component of thermally activated phonons (the two fluid model). The latter would contribute a diffusive component to the transport of S z . There’s lots of work on spin superfluidity built on this picture. Am I missing some piece of physics and/or the way the language of diffusion is used in this context?

Response: We thank the editor for pointing out this important issue. We agree with the referee that it is not correct to attribute diffusion/subdiffusion to the power-law decay of C xy ∼ 1/t α , since the planar components are not conserved. Our intention was to contrast the power-law exponent α < 1 with ‘diffusive’ power-law. However, the use of subdiffu- sive/subdiffusion is indeed not legitimate. We have modified all the related texts. We also agree that there will be both superflow and diffusive parts to the transport of conserved component S z below T KT . Indeed, we find evidence of both spin-wave component, originating from ∇φ, and diffusive component in C zz (t), as expected from model E dynamics (Ref.60). As a result, C zz (t) exhibits an oscillatory behaviour with power-law decay having exponent consistent with α ≈ 1 . However, the power-law exponent cannot be detected accurately due to the oscillatory behaviour of C zz (t).

List of changes

We have made the following changes in response to the referee and editor’s comments.
1. We have modified the sentences with multiple sub-clauses to improve the readability of
the introduction part.
2. We have corrected all the sentences where the power-law decay of C xy (t) in the Kosterlitz-
Thouless regime for the easy-plane case was referred as ’subdiffusive’ and/or ‘subdiffu-
3. We have updated the references with the citations to the latest published articles.

Published as SciPost Phys. 11, 087 (2021)

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