We study stability of the Sachdev-Ye-Kitaev (${\mathrm{SYK}}_4$) 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 ${\mathrm{SYK}}_2$ perturbation and demonstrate stability of the ${\mathrm{SYK}}_4$ infrared 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.

• Received 14 June 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.236601