Eigenstate entanglement in the Sachdev-Ye-Kitaev model

TL;DR

This paper analyzes the entanglement entropy of eigenstates in the Sachdev-Ye-Kitaev model, deriving an analytical volume law coefficient that depends on energy density and subsystem size, confirmed by recent numerical results.

Contribution

It provides an analytical calculation of the entanglement entropy volume law coefficient in the SYK model, linking it to the density of states and subsystem parameters.

Findings

Entanglement entropy follows a volume law in the SYK model.

The volume law coefficient depends on energy density and subsystem size.

Numerical results confirm the analytical predictions.

Abstract

We study the entanglement entropy of eigenstates (including the ground state) of the Sachdev-Ye-Kitaev model. We argue for a volume law, whose coefficient can be calculated analytically from the density of states. The coefficient depends on not only the energy density of the eigenstate but also the subsystem size. Very recent numerical results of Liu, Chen, and Balents confirm our analytical results.