Absence of Fast Scrambling in Thermodynamically Stable Long-Range Interacting Systems

Tomotaka Kuwahara, Keiji Saito

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as R-α, where R 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 α. In this regard, a crucial open challenge is to identify the optimal condition for α such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with α>D (D: 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 α>D and the necessary scrambling time over a distance R is larger than t≳R[(2α-2D)/(2α-D+1)].

Original languageEnglish
Article number030604
JournalPhysical review letters
Issue number3
Publication statusPublished - 2021 Jan 22

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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