Non-Fermi liquid behavior in the Sachdev-Ye-Kitaev model for a one dimensional incoherent semimetal

TL;DR

This paper investigates a 1+1D two-band SYK model representing a quadratic semimetal, revealing a novel non-Fermi liquid state with unique temperature-dependent resistivity through analytical and numerical methods.

Contribution

It introduces a dispersive SYK model for a quadratic band touching semimetal and characterizes its non-Fermi liquid behavior using a combined analytical and numerical approach.

Findings

Identifies a non-Fermi liquid with resistivity $ ho\,\propto T^{2/5}$

Shows the model's fixed point corresponds to a dispersive SYK state

Uses scaling symmetry to analyze the strongly dispersive limit

Abstract

Abstract We study a two-band dispersive Sachdev-Ye-Kitaev (SYK) model in 1 + 1 dimension. We suggest a model that describes a semimetal with quadratic dispersion at half-filling. We compute the Green's function at the saddle point using a combination of analytical and numerical methods. Employing a scaling symmetry of the Schwinger-Dyson equations that becomes transparent in the strongly dispersive limit, we show that the exact solution of the problem yields a distinct type of non-Fermi liquid with sublinear $\rho\propto T^{2/5}$ temperature dependence of the resistivity. A scaling analysis indicates that this state corresponds to the fixed point of the dispersive SYK model for a quadratic band touching semimetal.