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Operator Levy Flight: Light Cones in Chaotic Long-Range Interacting Systems

TitleOperator Levy Flight: Light Cones in Chaotic Long-Range Interacting Systems
Publication TypeJournal Article
Year of Publication2020
AuthorsT. Zhou, S. Xu, X. Chen, A. Guo, and B. Swingle
JournalPhys. Rev. Lett.
Volume124
Pagination180601
Date PublishedMAY 4
Type of ArticleArticle
ISSN0031-9007
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 a 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 >= d + 1/2. We also provide a Levy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1D long-range spin models with 200 sites.

DOI10.1103/PhysRevLett.124.180601