A renormalization-group analysis of the interacting resonant level model at finite bias: Generic analytic study of static properties and quench dynamics

TL;DR

This paper employs a real-time renormalization group approach to analytically study the static properties and quench dynamics of a charge-fluctuating quantum dot model at finite bias, revealing power-law behaviors and relaxation phenomena.

Contribution

It develops a comprehensive RG framework for the interacting resonant level model, providing analytic expressions for key observables across various parameters, including asymmetric interactions.

Findings

Power-law behavior observed only as a function of gate voltage, not bias voltage.

Exponential relaxation with voltage-dependent oscillations in quench dynamics.

Analytic expressions for charge susceptibility, current, and conductance derived.

Abstract

Using a real-time renormalization group method we study the minimal model of a quantum dot dominated by charge fluctuations, the two-lead interacting resonant level model, at finite bias voltage. We develop a set of RG equations to treat the case of weak and strong charge fluctuations, together with the determination of power-law exponents up to second order in the Coulomb interaction. We derive analytic expressions for the charge susceptibility, the steady-state current and the conductance in the situation of arbitrary system parameters, in particular away from the particle-hole symmetric point and for asymmetric Coulomb interactions. In the generic asymmetric situation we find that power laws can be observed for the current only as function of the level position (gate voltage) but not as function of the voltage. Furthermore, we study the quench dynamics after a sudden switch-on of the level-lead couplings. The time evolution of the dot occupation and current is governed by exponential relaxation accompanied by voltage-dependent oscillations and characteristic algebraic decay.