Absence of Fast Scrambling in Thermodynamically Stable Long-Range Interacting Systems
- 22 January 2021
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 126 (3), 030604
- https://doi.org/10.1103/physrevlett.126.030604
Abstract
In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as , where is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate . In this regard, a crucial open challenge is to identify the optimal condition for such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with (: spatial dimension), where the total energy is extensive in terms of system size and the thermodynamic limit is well defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as and the necessary scrambling time over a distance is larger than .
Funding Information
- RIKEN
- Japan Society for the Promotion of Science (18K13475, JP16H02211, JP19H05603)
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