Correlation Functions and Chaotic Behavior of the SYK Chain Model in Pure States

TL;DR

This paper investigates the thermalization and scrambling of information in the SYK chain model's pure states, revealing that correlation functions and information scrambling behave thermally even in non-thermal eigenstates, challenging previous notions of slow thermalization.

Contribution

It provides the first detailed analysis of correlation functions and information scrambling in individual energy eigenstates of the SYK chain, showing they closely resemble thermal behavior.

Findings

Two-point correlation functions in eigenstates match thermal predictions

Information scrambling occurs efficiently in pure eigenstates

Slow thermalization does not affect all probes of thermalization

Abstract

Recent investigations of R\'enyi entanglement entropy in the SYK chain of Majorana fermions have indicated that the model exhibits slow thermalization when initialized in certain states. The extent to which the heavy modes -- believed to underlie this behavior -- affect other aspects of the model remains an open question. In this work, I study thermalization and scrambling of information in individual energy eigenstates of the SYK chain using exact diagonalization. I show that two-point correlation functions in finite-energy eigenstates closely match their thermal counterparts and that information scrambling occurs efficiently within these pure states. These results suggest that the slow thermalization observed in entanglement dynamics does not extend to all probes of thermalization and scrambling, even in pure states. I discuss the implications of these findings for thermal states in a potential holographic dual theory.