Sachdev-Ye-Kitaev model with quadratic perturbations: the route to a non-Fermi-liquid
We study stability of the SYK4 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 SYK2 perturbation and demonstrate stability of the SYK4 infra-red asymptotic behavior characterized by a Green function G(τ) ~ τ-3/2, with respect to weak quadratic perturbation. This result is supported by exact numerical diagornalization. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.
This work is done in collaboration with A. V. Lunkin and K. S. Tikhonov .