SciPost Submission Page

Kibble–Zurek mechanism in the Ising Field Theory

by K. Hódsági, M. Kormos

Submission summary

As Contributors: Márton Kormos
Preprint link: scipost_202007_00061v1
Date submitted: 2020-07-31 15:21
Submitted by: Kormos, Márton
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Quantum Physics
Approaches: Theoretical, Computational


The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in a genuinely interacting field theory. We demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities, including higher cumulants of the excess heat.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2020-8-5 Invited Report


The manuscript provides solution of the Kibble-Zurek problem in a genuinely interacting quantum field theory. This is a valuable extension that may open a new research avenue. The calculation involves approximations, naturally. The crucial one is the adiabatic perturbation theory (APT) whose validity is claimed to be justified for low density of excitations. However, comparison between the APT in Ref. [7] and an exact solution in Ref. [8] shows that in the transverse Ising chain the APT gives the correct power law for density of defects but its numerical prefactor is overestimated by 60%. This error occurs for low density of excitations that are obtained for long quench times and, therefore, the low density criterion is not sufficient to justify the APT. I would like the authors to make more thorough analysis of APT's applicability before the manuscript can be accepted for publication.

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

Anonymous Report 1 on 2020-8-3 Invited Report


The authors perform an in-depth study of the quantum Kibble-Zurek problem for the Ising Field Theory. They analyze a vast zoology of regimes and quench directions in the 2d coupling space, by employing advanced analytical and numerical techniques inspired by conformal field theory. The approach is well justified, and the results are well argumented and scientifically sound.


1. The delivery of take-away messages is somewhat mediocre: The most interesting results of the research are scattered throughout the text, partially hidden in the conclusion, and almost absent in the abstract.

2. The language is slightly too focused on statistical quantum mechanics: Even though the potential audience for this research may be broad, it feels that the adopted language relies on conformal field theory language more than it should.

3. Proposal of experiments missing: There is no mention how the additional knowledge made available by this study may impact or be verified on an experimental platform.


I will likely recommend publication after the authors consider my comments and suggestions.

Requested changes

To overcome the weaknesses I previously mentioned, I would suggest the following revision (using the same numbering as before):

1. Highlight the most important results better, in the abstract AND the conclusion.

2. Expand the heavy-CFT oriented arguments by making them more approachable for non-experts.

3. Consider if the results from this research can foster the design of new experiments, or can be verified in existing experiments, or if they explain previously-observed unsolved phenomena.

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

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