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Weak vs. strong breaking of integrability in interacting scalar quantum field theories

by Bence Fitos, Gábor Takács

This is not the latest submitted version.

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Submission summary

Authors (as registered SciPost users): Gabor Takacs
Submission information
Preprint Link:  (pdf)
Date submitted: 2023-05-18 11:21
Submitted by: Takacs, Gabor
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


The recently proposed classification of integrability-breaking perturbations according to their strength is studied in the context of quantum field theories. Using random matrix methods to diagnose the resulting quantum chaotic behaviour, we investigate the $\phi^4$ and $\phi^6$ interactions of a massive scalar, by considering the crossover between Poissonian and Wigner-Dyson distributions in systems truncated to a finite-dimensional Hilbert space. We find that a naive extension of the scaling of crossover coupling with the volume observed in spin chains does not give satisfactory results for quantum field theory. Instead, we demonstrate that considering the scaling of the crossover coupling with the number of particles yields robust signatures, and is able to distinguish between the strengths of integrability breaking in the $\phi^4$ and $\phi^6$ quantum field theories.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2023-8-7 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2305.02666v2, delivered 2023-08-07, doi: 10.21468/SciPost.Report.7619


1- The article is well-organized and thoughtfully written.
2- The topic is interesting.
2- The numerical results are convincing.


1- The justification given on page 7, about the use of the number of particles in the unperturbed theory, as a suitable approximate quantum number to study this crossover phenomena, appears to me slightly misleading.


This article focuses on the characterization of explicit integrability breaking in a 1+1-dimensional quantum field theory associated with a massive free boson perturbed by the operators $\phi^N$, with N=4 or N=6.

The analysis consists in the study of the spectrum of the corresponding Hamiltonian using the truncated space approximation to explore the crossover of the coupling as a function of the number of particles. This is in contrast to the case of spin chains, where the crossover was studied as a function of the volume.
The research topic is interesting, and the article is well-organized. The results have a numerical/phenomenological nature but are quite convincing.

My primary concern centres around the use of the number of particles from the undeformed theory as a "good approximate quantum number" instead of the volume.

This approach seems somewhat risky, as one could argue that the crossover phenomena should be closely tied to the rapid increase in non-elastic processes. From my perspective, the justification presented on page 7—where the authors correctly assert that violating particle number processes are suppressed at low energies—may not be fully applicable in the current context.

In my view, a more thorough justification is needed for solely considering the interacting Hamiltonians within individual subspaces of a given particle number $n$.

Still, the obtained results do indeed appear convincing.

Requested changes

1-Improve/correct the central paragraph on page 7.

2-Provide concrete --comparative-- numerical support for considering the interacting Hamiltonians only within individual subspaces of a given particle number $n$.

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

Anonymous Report 1 on 2023-7-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2305.02666v2, delivered 2023-07-23, doi: 10.21468/SciPost.Report.7552


1 - original and relevant
2 - up to date and of current interest
3 - the flow of reasoning can be followed very clearly
4 - presentation of results is well documented and understandable
5 - citations of previous literature are correct




The paper deals with the classification of integrability breaking perturbations according to their strength, exploring $\phi^4$ and $\phi^6$ quantum field theories, by methods of Truncated Hamiltonian Approach (THA), an evolution/adaptation of TCSA, of which the authors are experts.
The recently introduced criteria for the classification of integrability breaking make this paper very relevant, current and original.
It is written clearly and the line of reasoning can be followed with ease. The results presented are well complemented by the show of graphs and tables of data, well commented by captions and therefore easy to read and interpret.
The citations to previous literature are, to my knowledge, correct and complete.
For all these reasons, and because the contents fit with the interests of the journal, I strongly support the publication of this paper on SciPost Physics.

Requested changes


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

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