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

Tomotaka Kuwahara; Keiji Saito

doi:10.1103/PhysRevLett.126.030604

paper

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

arXiv:2009.10124 · doi: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 $R^{- α}$ , 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 $t ≳ R^{\frac{2 α - 2 D}{2 α - D + 1}}$ .

arXiv comment8 pages + 20 pages, 9 figures. [v.2] Title is changed. Typos are corrected and readability is improved. [v.3] published version

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

Abstract

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