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

TL;DR

This paper investigates the tunneling spectroscopy of the SYK model, revealing a voltage duality in conductance that signals underlying conformal symmetry in a strongly correlated quantum system.

Contribution

It introduces a duality relation in the differential conductance of the SYK model, linking low and high voltage regimes and providing a new signature of conformal symmetry.

Findings

Discovered a voltage duality in conductance, G(ξ)=G(π/ξ).

Established a one-parameter scaling law in the conformal regime.

Linked non-Fermi liquid behavior to tunneling spectroscopy signatures.

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.