The operator Lévy flight: light cones in chaotic long-range interacting systems

Abstract

We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension $d$ and the exponent $\alpha$ governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for $\alpha \ge d+1/2$. We also provide a Lévy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1d long-range spin models with 200 sites.

published version: improved presentation of the scaling analysis around Tab. I, additional data in Fig. 3

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