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Adiabatic gauge potential and integrability breaking with free fermions
by Balázs Pozsgay, Rustem Sharipov, Anastasiia Tiutiakina, István Vona
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Balázs Pozsgay |
| Submission information | |
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| 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 | |
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| Academic field: | Physics |
| Specialties: |
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| 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.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
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)