TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.244
TI  - Temporal fluctuations of correlators in integrable and chaotic quantum systems
PY  - 2023/12/18
UR  - https://scipost.org/SciPostPhys.15.6.244
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 244
A1  - L. M. Lezama, Talía
AU  - Bar Lev, Yevgeny
AU  - Santos, Lea F.
AB  - We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies. For physical initial states, our bounds predict the exponential decay of the temporal fluctuations as a function of the system size. We numerically verify this prediction for chaotic and interacting integrable spin-1/2 chains, which satisfy the assumption of our bounds. On the other hand, we show analytically and numerically that for the XX model, which is a noninteracting system with gap degeneracies, the temporal fluctuations decay polynomially with system size for operators that are local in the fermion representation and decrease exponentially in the system size for non-local operators. Our results demonstrate that the decay of the long-time temporal fluctuations of correlators cannot be used as a reliable metric of chaos or lack thereof.
ER  -

@Article{10.21468/SciPostPhys.15.6.244,
	title={{Temporal fluctuations of correlators in integrable and chaotic quantum systems}},
	author={Talía L. M. Lezama and Yevgeny Bar Lev and Lea F. Santos},
	journal={SciPost Phys.},
	volume={15},
	pages={244},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.244},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.244},
}