Abstract

We study 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 perturbation and demonstrate stability of the SYK_4 infra-red asymptotic behavior characterized by a Green function G(t) ~ t^(-3/2), with respect to weak quadratic perturbation. This result is supported by numerical exact diagonalization and solution of the mean-field equations. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.