TY - JOUR T1 - The operator Lévy flight: light cones in chaotic long-range interacting systems JF - Phys. Rev. Lett. Y1 - 2020 A1 - Tianci Zhou A1 - Shenglong Xu A1 - Xiao Chen A1 - Andrew Guo A1 - Brian Swingle AB -

We propose a generic light cone phase diagram for chaotic long-range r−α interacting systems, where a linear light cone appears for α≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the Lévy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites. 

VL - 124 UR - https://arxiv.org/abs/1909.08646 CP - 180601 U5 - https://doi.org/10.1103/PhysRevLett.124.180601 ER -