Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model

TL;DR

This paper investigates the relationship between stabilizer entropy and entanglement in the SYK model, revealing complex entanglement patterns in the chaotic regime and contrasting behavior in the integrable limit.

Contribution

It provides a detailed analysis of stabilizer Rènyi entropy and entanglement spectrum in the SYK model, highlighting the complexity of quantum resources in chaotic versus integrable regimes.

Findings

SYK4 exhibits complex entanglement and stabilizer resource patterns

SYK2 shows non-universal, less complex entanglement features

Interplay between entanglement and stabilizer entropy varies with model interpolation

Abstract

The Sachdev-Ye-Kitaev (SYK) model is of paramount importance for the understanding of both strange metals and a microscopic theory of two-dimensional gravity. We study the interplay between Stabilizer R\'enyi Entropy (SRE) and entanglement entropy in both the ground state and highly excited states of the SYK4+SYK2 model interpolating the highly chaotic four-body interactions model with the integrable two-body interactions one. The interplay between these quantities is assessed also through universal statistics of the entanglement spectrum and its anti-flatness. We find that SYK4 is indeed characterized by a complex pattern of both entanglement and non-stabilizer resources while SYK2 is non-universal and not complex. We discuss the fragility and robustness of these features depending on the interpolation parameter.