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

• Received 7 March 2018
• Revised 12 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.115122