Quantum Entanglement of the Sachdev-Ye-Kitaev Models

Understand

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model of fermions interacting with $q$-body random couplings.

• For $q=2$, it describes free particles, and is non-chaotic in the many-body sense, while for $q>2$ it is strongly interacting and exhibits many-body chaos.
• In this work we study the entanglement entropy (EE) of the SYK$q$ models, for a bipartition of $N$ real or complex fermions into subsystems containing $2m$ real/$m$ complex fermions and $N-2m$/$N-m$ fermions in the remainder.
• For the free model SYK$2$, we obtain an analytic expression for the EE, derived from the $\beta$-Jacobi random matrix ensemble.