Quenched Kitaev Chain: Analogous model of Gravitational Collapse

TL;DR

This paper studies the thermalization process in a free Fermionic chain after a sudden quench, analyzing how local observables evolve and relax, and demonstrating the formation of a light cone consistent with Lieb-Robinson bounds.

Contribution

It provides an analytical and numerical investigation of generalized thermalization and light cone formation in a quenched free Fermionic chain, highlighting the irrelevance of internal interactions for strong quenches.

Findings

Observables relax to a generalized Gibbs ensemble in the thermodynamic limit.

The evolution of observables forms a light cone consistent with Lieb-Robinson bounds.

Internal interactions become negligible after a sufficiently strong quench.

Abstract

We investigate generalized thermalization in an isolated free Fermionic chain evolving from an out of equilibrium initial state through a sudden quench. We consider the quench where a Fermionic chain is broken into two disjoint chains. We focus on the evolution of the local observables namely, occupation number, nearest neighbor hopping, information sharing and out-of-time-order correlations after the quench and study the relaxation of the observable, leading to generalized Gibbs ensemble for the system in the thermodynamic limit though it has been argued that non-interacting or free Fermionic models in general do not relax to GGE. We obtain the light cone formed by the evolution of the observables along the Fermionic lattice chain due to the sudden quench which abides by the Lieb-Robinson bound in quantum systems. We also analytically study a simpler model which captures the essential features of the system. Our analysis strongly suggests that the internal interactions within the system do not remain of much importance once the quench is sufficiently strong.