### The operator Lévy flight: light cones in chaotic long range interacting systems (Jan. 3, 2020)

• Published: 2020-01-02

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

Speaker: Tianci Zhou (KITP, UCSB)

Time: Jan. 3, 2020, 10:00 am

Abstract: Long-range interactions are common in many laboratory settings, including Rydberg atoms and systems with dipolar interactions. In this work, we study the emergent speed limit for information spreading in generic power-law long-range interacting systems. Assuming the dephasing nature of quantum chaos, we map the dynamics of the out-of-time ordered correlation function to a classical stochastic process and obtain an exact phase diagram of the light cone shape in terms of the exponent $\alpha$ defining the power-law interactions. In particular, in $d$-dimension a linear light cone results when $\alpha \ge d + 1/2$. We provide a simple L\'evy flight interpretation of the phase diagram and show consistent numerical data for 1d long-range spin models with 200 sites.