07.10.2020 (Wednesday)

The butterfly effect away from maximal chaos

Regular Seminar Gabor Sarosi (CERN)

13:15 KCL
room Zoom

A simple probe of chaos and operator growth in many-body quantum systems is the thermal out of time ordered (OTO) four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside a so called butterfly cone. I will discuss universal features of the spatiotemporal structure of this exponential growth in large N systems. In particular I will argue that there can be a smaller, “scramblon” cone inside the butterfly cone. Outside the scramblon cone, the growth of the OTO four point function is completely universal and saturates a chaos bound. I will explain the connection to conformal Regge theory, where crossing the scramblon cone is related to an exchange of dominance between the pomeron and the stress tensor. Finally, I will discuss a connection between chaos and energy transport, called the pole skipping phenomenon, which is a subtle effect in the thermal energy density retarded two point function at a special point in the complex frequency and momentum planes. I will present an improved understanding of this connection and test it in the large q limit of an SYK chain, where I determine both the Lyapunov growth of the OTO correlator and the energy density two point function exactly as a function of the coupling, interpolating between weekly coupled and maximally chaotic behaviour. [For the Zoom link, please email to: alejandro.cabo_bizet@kcl.ac.uk ]