Low-rank Sachdev-Ye-Kitaev models

TL;DR

This paper explores a family of solvable low-rank Sachdev-Ye-Kitaev models with tunable coupling matrices, classifying their quantum phases and analyzing their chaotic and non-Fermi liquid behaviors.

Contribution

It provides a complete classification of quantum phases in low-rank SYK models and examines how eigenvalue distributions influence their properties.

Findings

Identified phases with continuous fermion scaling dimensions.

Showed these phases are maximally chaotic with specific coupling matrix conditions.

Discovered generic distributions lead to almost Fermi liquids with distinct decay rates.

Abstract

Motivated by recent works on atom-cavity realizations of fast scramblers, and on Cooper pairing in non-Fermi liquids, we study a family of solvable variants of the ($q=4$) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate {an extensively degenerate or negative semidefinite coupling matrix}. More generic distributions give rise to "almost Fermi liquids" with a scaling dimension $\Delta = 1/2$, but which differ from a genuine Fermi-liquid in quasi-particle decay rate, quantum Lyapunov exponent and/or specific heat.