SYK model with quadratic perturbations: the route to a non-Fermi-liquid

Abstract

We study the stability of the SYK${}_4$ model with a large but finite number of fermions $N$ with respect to a perturbation, quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the SYK${}_2$ perturbation and demonstrate the stability of the SYK${}_4$ infra-red asymptotic behavior characterized by a Green function $G(\tau )\propto 1/{\tau }^{3/2}$, with respect to weak perturbation. This result is supported by exact numerical diagonalization. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.

13 pages and 2 figures