Solvable model for quantum criticality between Sachdev-Ye-Kitaev liquid and disordered Fermi liquid

Abstract

We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle point solutions at large number $N$ of fermions are obtained and show a characteristic scale-invariant $\sim |\omega {|}^{-1/2}$ behavior of the spectral function below the transition which is replaced by a $\sim |\omega {|}^{-1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle point equations and discussed in the broader context of the field.

5 pages, 2 figures plus appendices

References in corpus (4)

• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• More on Supersymmetric and 2d Analogs of the SYK Model
• Higher Dimensional Generalizations of the SYK Model
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath