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 .
- Received 9 October 2020
- Accepted 22 December 2020
DOI:https://doi.org/10.1103/PhysRevLett.126.030604
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