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arXiv · 2009.10124

Absence of fast scrambling in thermodynamically stable long-range interacting systems

Tomotaka Kuwahara·Keiji Saito
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Abstract

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

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BibTeXRIS

Tomotaka Kuwahara, Keiji Saito. 2020-09-21. Absence of fast scrambling in thermodynamically stable long-range interacting systems. https://doi.org/10.1103/physrevlett.126.030604

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