SYK model with quadratic perturbations: the route to a non-Fermi-liquid
Abstract
We study the 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 the stability of the SYK4 infra-red asymptotic behavior characterized by a Green function G(τ) 1/τ3/2 , 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.
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