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: |
2017 |
Typology: |
1.01 - Original Scientific Article |
Organization: |
UL FMF - Faculty of Mathematics and Physics |
Publisher: |
American Physical Society |
UDC: |
530.145 |
COBISS: |
3179364
|
ISSN: |
2469-9950 |
Views: |
1192 |
Downloads: |
575 |
Average score: |
0 (0 votes) |
Metadata: |
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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 |