Functional renormalization group study of the interacting resonant level model in and out of equilibrium

TL;DR

This paper applies a generalized functional renormalization group approach to study non-equilibrium transport in the interacting resonant level model, revealing power-law decay of current at symmetric points and complex behavior near resonant energies.

Contribution

It introduces a Keldysh frequency space extension of the functional renormalization group for quantum impurity systems out of equilibrium, benchmarking it against DMRG data.

Findings

Steady-state current decays as a power law with bias voltage at particle-hole symmetry.

The exponent of decay depends on Coulomb interaction strength.

Complex current-voltage relations occur when the level energy is near chemical potentials.

Abstract

We investigate equilibrium and steady-state non-equilibrium transport properties of a spinless resonant level locally coupled to two conduction bands of width ~\Gamma via a Coulomb interaction U and a hybridization t'. In order to study the effects of finite bias voltages beyond linear response, a generalization of the functional renormalization group to Keldysh frequency space is employed. Being mostly unexplored in the context of quantum impurity systems out of equilibrium, we benchmark this method against recently-published time-dependent density matrix renormalization group data. We thoroughly investigate the scaling limit \Gamma\to\infty characterized by the appearance of power laws. Most importantly, at the particle-hole symmetric point the steady-state current decays like J ~ V^{-\alpha_J} as a function of the bias voltage V>>t', with an exponent \alpha_J(U) that we calculate to leading order in the Coulomb interaction strength. In contrast, we do not observe a pure power-law (but more complex) current-voltage-relation if the energy \epsilon of the resonant level is pinned close to either one of the chemical potentials \pm V/2.