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Adiabatic gauge potential and integrability breaking with free fermions

by Balázs Pozsgay, Rustem Sharipov, Anastasiia Tiutiakina, István Vona

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Submission summary

Authors (as registered SciPost users): Balázs Pozsgay
Submission information
Preprint Link: scipost_202408_00008v1  (pdf)
Date accepted: 2024-08-30
Date submitted: 2024-08-09 11:27
Submitted by: Pozsgay, Balázs
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

We revisit the problem of integrability breaking in free fermionic quantum spin chains. We investigate the so-called adiabatic gauge potential (AGP), which was recently proposed as an accurate probe of quantum chaos. We also study the so-called weak integrability breaking, which occurs if the dynamical effects of the perturbation do not appear at leading order in the perturbing parameter. A recent statement in the literature claimed that integrability breaking should generally lead to an exponential growth of the AGP norm with respect to the volume. However, afterwards it was found that weak integrability breaking is a counter-example, leading to a cross-over between polynomial and exponential growth. Here we show that in free fermionic systems the AGP norm always grows polynomially, if the perturbation is local with respect to the fermions, even if the perturbation strongly breaks integrability. As a by-product of our computations we also find, that in free fermionic spin chains there are operators which weakly break integrability, but which are not associated with known long range deformations.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Author comments upon resubmission

Referee 2. understands the situation correctly. The only minor addition from us is that in Section 4.3 we show that the AGP is exponentially growing if the operator is non-local in the fermions, and this holds already for $\lambda=0$.

List of changes

We added the missing coupling constant $\lambda$ to eq. (76).
Also, we added a sentence to the Conclusions:
"In contrast, the AGP is exponentially growing if the perturbation is non-local in the fermions, and this holds already for the unperturbed model with $\lambda=0$."

Published as SciPost Phys. 17, 075 (2024)


Reports on this Submission

Anonymous Report 1 on 2024-8-10 (Invited Report)

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I recommend publication of the revised version. No further changes are required.

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Publish (easily meets expectations and criteria for this Journal; among top 50%)

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