Universal dynamics of Sachdev-Ye-Kitaev model

Abstract

The Sachdev-Ye-Kitaev (SYK) model was introduced in the context of explaining the properties of “strange metals,” and has been found to manifest the characteristics of a quantum theory which is holographically dual to extremal charged black holes with two-dimensional anti-de Sitter horizons. Black holes are the best known scramblers of quantum information in nature, a feature shared by the SYK model, which has triggered a massive interest in its dynamics. Yet, many questions about the dynamics of the SYK model remain open. In this talk, we shall be discussing the equilibration process of a fermionic system under the SYK Hamiltonian evolution. Our study, based on a state-of-the-art exact diagonalization method, reveals that the system exhibits a super-exponential universal equilibration dynamics. By devising a master equation for disordered systems, we successfully explain some of the key features of this dynamics. We infer the universality from the spectral analysis of the corresponding Lindbladian. We expect our findings shed light on challenging questions for systems far from equilibrium, such as, thermalization of closed and disordered quantum systems.