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arXiv · 1909.08646

The operator L\'evy flight: light cones in chaotic long-range interacting systems

Tianci Zhou·Shenglong Xu·Xiao Chen·Andrew Guo·Brian Swingle
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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 L\'evy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1d long-range spin models with 200 sites.

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Tianci Zhou, Shenglong Xu, Xiao Chen, Andrew Guo, Brian Swingle. 2019-09-18. The operator L\'evy flight: light cones in chaotic long-range interacting systems. https://doi.org/10.1103/physrevlett.124.180601

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