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

TL;DR

This paper investigates the stability of the SYK$_4$ model against quadratic perturbations, demonstrating that its non-Fermi-liquid behavior remains stable under weak perturbations, supported by analytic and numerical methods.

Contribution

The authors develop an analytic perturbation theory for the SYK$_4$ model with quadratic perturbations and establish its stability, advancing understanding of non-Fermi-liquid states.

Findings

SYK$_4$ model's infra-red behavior is stable under weak quadratic perturbations

Green function retains $1/\tau^{3/2}$ form despite perturbations

Numerical diagonalization confirms analytic stability results

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.