Low-High Voltage Duality In Tunneling Spectroscopy Of The Sachdev-Ye-Kitaev Model

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 = eV J/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.