Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model

Abstract

The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated metal with all-to-all random interactions (average strength $J$) between $N$ fermions (complex Dirac fermions or real Majorana fermions). In the large-$N$ limit a conformal symmetry emerges that renders the model exactly soluble. Here we study how the non-Fermi liquid behavior of the closed system in equilibrium manifests itself in an open system out of equilibrium. We calculate the current-voltage characteristic of a quantum dot, described by the complex-valued SYK model, coupled to a voltage source via a single-channel metallic lead (coupling strength $\Gamma$). A one-parameter scaling law appears in the large-$N$ conformal regime, where the differential conductance $G=dI/dV$ depends on the applied voltage only through the dimensionless combination $\xi=eVJ/\Gamma^2$. Low and high voltages are related by the duality $G(\xi)=G(\pi/\xi)$. This provides for an unambiguous signature of the conformal symmetry in tunneling spectroscopy.