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

by Bence Fitos, Gábor Takács

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Gabor Takacs
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-08-31
Date submitted: 2023-08-21 12:25
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.

Author comments upon resubmission

We are grateful to the referees for the careful reading of our manuscript.

We agree with Referee 2 that our discussion regarding the role of particle numbers was not written with enough care, and we replaced the corresponding text with a more careful argument. We thank the referee for pointing this out. We note further that the whole argument is admittedly heuristic but is justified by our subsequent findings.

List of changes

2nd and 3rd paragraphs of Section 4 were rewritten to make our point more precise and extended the sentence after Eq. (4.1).

Published as SciPost Phys. 15, 137 (2023)

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