Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model

TL;DR

This paper investigates the nonequilibrium dynamics of a mixed Sachdev-Ye-Kitaev model, revealing how different quench protocols influence thermalization, effective temperature, and prethermalization phenomena in a system with competing chaotic and Fermi liquid behaviors.

Contribution

It provides a detailed analysis of quench-induced thermalization and prethermalization in a mixed SYK model, highlighting the impact of quench parameters on effective temperature and relaxation.

Findings

The model thermalizes to a finite temperature equilibrium.

Effective temperature can be tuned below or above the Fermi-liquid to Non-Fermi-liquid crossover.

Certain quench protocols exhibit significantly slowed heating, indicating prethermalization.

Abstract

We study the nonequilibrium quench dynamics of a mixed Sachdev-Ye-Kitaev model, with competing two bodies random interactions leading to maximally chaotic Non-Fermi Liquid dynamics and a single body term which dominates at low temperatures and leads to Fermi liquid behavior. For different quench protocols, including sudden switching of two-body interaction and double quench protocols, we solve the large $N$ real-time Dyson equation on the Keldysh contour and compute the dynamics of Green's functions from which we obtain effective temperature and relaxation rates. We show that the model thermalizes to a finite temperature equilibrium and that depending on the value of the quench parameters the effective temperature can be below or above the Fermi-Liquid to Non-Fermi Liquid crossover scale, which can then be accessed through the nonequilibrium dynamics. We identify quench protocols for which the heating dynamics slow down significantly, an effect that we interpret as a signature of prethermalization.