Deviations from maximal entanglement for eigenstates of the Sachdev-Ye-Kitaev model

TL;DR

This paper proves that mid-spectrum eigenstates of the SYK model have entanglement entropy significantly less than the maximum, revealing fundamental differences from random states and highlighting unique entanglement properties.

Contribution

It establishes a rigorous lower bound on the deviation of entanglement entropy from maximum for eigenstates of the SYK model.

Findings

Entanglement entropy deviates from maximum by a positive constant for certain subsystems.

Mid-spectrum eigenstates differ fundamentally from random states in entanglement properties.

The result provides insight into the structure of eigenstates in the SYK model.

Abstract

We consider mid-spectrum eigenstates of the Sachdev-Ye-Kiteav (SYK) model. We prove that for subsystems whose size is a constant fraction of the system size, the entanglement entropy deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of the SYK model and that of random states.