Quantum ergodicity in the SYK model

Abstract

In my talk I will discuss a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales [1]. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime describable by random matrix theory (RMT). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which can be identified as the generators of the Clifford algebra: each of the 2^N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system’s approach to the ergodic long time regime. I will present a number of analytical results for various spectral correlation functions which characterise the dynamics of the SYK model and demonstrate their favorable agreement with existing numerical data. [1] A. Altalnd and D. Bagrets, Nucl. Phys. B 930, 45-68 (2018)