Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit

TL;DR

This paper investigates how a closed Majorana SYK system thermalizes after a quench, demonstrating that it reaches thermal equilibrium characterized by Green's functions and energy, with detailed analytical and numerical methods.

Contribution

The study introduces a detailed analytical framework and numerical algorithm for analyzing thermalization in a large-$q$ SYK model after a quench.

Findings

The system reaches thermal equilibrium with respect to Green's functions and energy.

Derived and solved Kadanoff-Baym equations for the SYK model.

Revealed rich thermalization dynamics in a closed quantum system.

Abstract

The question of thermalization of a closed quantum system is of central interest in non-equilibrium quantum many-body physics. Here we present one such study analyzing the dynamics of a closed coupled Majorana SYK system. We have a large-$q$ SYK model prepared initially at equilibrium quenched by introducing a random hopping term, thus leading to non-equilibrium dynamics. We find that the final stationary state reaches thermal equilibrium with respect to the Green's functions and energy. Accordingly, the final state is characterized by calculating its final temperature and the thermalization rate. We provide a detailed review of analytical methods and derive the required Kadanoff-Baym equations, which are then solved using the algorithm developed in this work. Our results display rich thermalization dynamics in a closed quantum system in the thermodynamic limit.