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arXiv · 1806.11211

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

A. V. Lunkin·K. S. Tikhonov·M. V. Feigel'man
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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.

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A. V. Lunkin, K. S. Tikhonov, M. V. Feigel'man. 2018-06-28. SYK model with quadratic perturbations: the route to a non-Fermi-liquid. https://doi.org/10.1103/physrevlett.121.236601

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