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

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 SYK4 (with quartic couplings), which is maximally chaotic in the large system size limit, satisfies the standard ETH scaling while SYK2 (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