Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models

TL;DR

This paper investigates how eigenstate thermalization behaves in Sachdev-Ye-Kitaev Majorana models, revealing that chaotic SYK4 models satisfy ETH while integrable SYK2 models do not, with different effects observed when mixing the two.

Contribution

It demonstrates ETH validity in chaotic SYK4 models and its failure in integrable SYK2 models, analyzing the transition from chaos to integrability.

Findings

SYK4 satisfies ETH scaling in large systems

SYK2 does not satisfy ETH

Mixing SYK4 and SYK2 affects low- and high-energy properties differently

Abstract

The eigenstate thermalization hypothesis (ETH) is a conjecture on the nature of isolated quantum systems that guarantees the thermal behavior of subsystems when it is satisfied. ETH has been tested in various forms on a number of local many-body interacting systems. Here we examine the validity of ETH in a class of nonlocal disordered many-body interacting systems --- the Sachdev-Ye-Kitaev Majorana (SYK) models --- that may be tuned from chaotic behavior to integrability. Our analysis shows that SYK$_4$ (with quartic couplings), which is maximally chaotic in the large system size limit, satisfies the standard ETH scaling while SYK$_2$ (with quadratic couplings), which is integrable, does not. We show that the low-energy and high-energy properties are affected drastically differently when the two Hamiltonians are mixed.