Low-rank Sachdev-Ye-Kitaev models
Jaewon Kim, Xiangyu Cao, Ehud Altman
Abstract
Motivated by recent proposals of experimental realization of fast scramblers, 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 $\mathrm{\ensuremath{\Delta}}=1/2$, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.