TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.3.075
TI  - Adiabatic gauge potential and integrability breaking with free fermions
PY  - 2024/09/09
UR  - https://scipost.org/SciPostPhys.17.3.075
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 3
SP  - 075
A1  - Pozsgay, Balázs
AU  - Sharipov, Rustem
AU  - Tiutiakina, Anastasiia
AU  - Vona, István
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.17.3.075,
	title={{Adiabatic gauge potential and integrability breaking with free fermions}},
	author={Balázs Pozsgay and Rustem Sharipov and Anastasiia Tiutiakina and István Vona},
	journal={SciPost Phys.},
	volume={17},
	pages={075},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.3.075},
	url={https://scipost.org/10.21468/SciPostPhys.17.3.075},
}