Ivan Kukuljan (Author), Sašo Grozdanov (Author), Tomaž Prosen (Author)

Abstract

Out-of-time-ordered correlation functions (OTOCs) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local operators are bounded, an OTOC of local observables is bounded as well and thus its exponential growth is merely transient. As a better measure of quantum chaos in such systems, we propose, and study, the density of the OTOC of extensive sums of local observables, which can exhibit indefinite growth in the thermodynamic limit. We demonstrate this for the kicked quantum Ising model by using large-scale numerical results and an analytic solution in the integrable regime. In a generic case, we observe the growth of the OTOC density to be linear in time. We prove that this density in general, locally interacting, nonintegrable quantum spin and fermionic dynamical systems exhibits growth that is at most polynomial in time—a phenomenon, which we term weak quantum chaos. In the special case of the model being integrable and the observables under consideration quadratic, the OTOC density saturates to a plateau.

Keywords

kvantna mehanika;teorija kaosa;quantum mechanics;quantum chaos;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: American Physical Society
UDC: 530.145
COBISS: 3179364 Link will open in a new window
ISSN: 2469-9950
Views: 1192
Downloads: 575
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Other data

Secondary language: Slovenian
Secondary keywords: kvantna mehanika;teorija kaosa;
Pages: str. 060301-1-060301-6
Volume: ǂVol. ǂ96
Issue: ǂiss. ǂ6
Chronology: 2017
DOI: 10.1103/PhysRevB.96.060301
ID: 10915643