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

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• Quenched vs Annealed: Glassiness from SK to SYK
• Quantum tunneling dynamics in a complex-valued Sachdev-Ye-Kitaev model quench-coupled to a cool bath
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Towards quantum simulation of Sachdev-Ye-Kitaev model
• A proposal to extract and enhance four-Majorana interactions in hybrid nanowires