A Numerical Analysis of Thermalization in the Sachdev-Ye-Kitaev Model

Christopher T. Olund, Norman Y. Yao, Joel E. Moore

Anonymous

Andreas Eberlein, Valentin Kasper, Subir Sachdev A +1 more

We describe the nonequilibrium quench dynamics of the Sachdev-Ye-Kitaev models of fermions with random all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that, at long times, the fermion two-point function has a thermal form at a final temperature determined by energy conservation, and the numerical analysis is consistent with a thermalization rate proportional to this temperature. We also obtain an exact analytic solution of the quench dynamics in the large $q$ limit of a model with $q$ fermion interactions: in this limit, the thermalization of the two-point function is instantaneous.

譲治 那須, Joji Nasu, 幸年 求 +2 more

Grigory Tarnopolsky

We consider the Sachdev-Ye-Kitaev (SYK) model, where interaction involves $q$ fermions at a time. We find the $1/{q}^{2}$ correction to the thermal two-point function in the large $q$ expansion. Using this result, we find the $1/{q}^{3}$ correction to the SYK free energy.

Masudul Haque, Paul McClarty

This work addresses the question of whether the eigenstate thermalization hypothesis in its scaling form is satisfied in Sachdev-Ye-Kitaev models.Going substantially beyond previous treatments of eigenstate expectation values in such models, the authors present a scaling analysis and identify the situations where eigenstate thermalization holds and where it does not.