Matter Coupling of Dirac Matter in the Context of the SYK Model: Non-Gaussian Random Couplings and Bulk Mass Deformations

TL;DR

This paper extends the SYK model by incorporating non-Gaussian matter couplings and bulk fermion mass effects, analyzing their impact on spectral and entanglement properties.

Contribution

It introduces non-Gaussian coupling distributions and bulk mass into the SYK model, exploring their effects on spectral statistics and boundary interactions.

Findings

Average adjacent gap ratio depends on coupling distribution

Bulk mass affects boundary coupling but not spectral statistics

Qualitative behavior remains similar to Gaussian, massless case

Abstract

We elaborate further on the matter coupling of Dirac matter in the SYK framework, incorporating non-Gaussian coupling distributions and bulk fermion mass effects. Our study analyzes quartic matter couplings generated by a non-Gaussian distribution as an illustrative example. The introduction of bulk-fermion mass alters the boundary coupling between the Dirac and Majorana fermions. The averaged adjacent gap ratio is sensitive to the distribution of random couplings, which remains independent of the Hamiltonian's symmetry. The generalization of the SYK model to non-Gaussian distributions and the inclusion of bulk fermion mass remain qualitatively similar to the Gaussian and massless cases. Key deviations are observed only in the time scales for the linear ramp in the spectral form factor and the saturation of entanglement entropy.