Nonequilibrium functional RG with frequency dependent vertex function: A study of the single impurity Anderson model

TL;DR

This paper develops a nonequilibrium functional renormalization group method with frequency-dependent vertices to study the single impurity Anderson model, achieving accurate results for conductance and Kondo physics in weak to intermediate interactions.

Contribution

It introduces a novel fRG approach using level broadening as a flow parameter and accounts for frequency dependence of the two-particle vertex, improving nonequilibrium analysis of the model.

Findings

Excellent agreement with NRG for linear conductance in equilibrium.

Good agreement with TD-DMRG for nonequilibrium current.

Demonstrates the exponential scale of the Kondo temperature in the second derivative of the self-energy.

Abstract

We investigate nonequilibrium properties of the single impurity Anderson model by means of the functional renormalization group (fRG) within Keldysh formalism. We present how the level broadening Gamma/2 can be used as flow parameter for the fRG. This choice preserves important aspects of the Fermi liquid behaviour that the model exhibits in case of particle-hole symmetry. An approximation scheme for the Keldysh fRG is developed which accounts for the frequency dependence of the two-particle vertex in a way similar but not equivalent to a recently published approximation to the equilibrium Matsubara fRG. Our method turns out to be a flexible tool for the study of weak to intermediate on-site interactions U <= 3 Gamma. In equilibrium we find excellent agreement with NRG results for the linear conductance at finite gate voltage, magnetic field, and temperature. In nonequilibrium, our results for the current agree well with TD-DMRG. For the nonlinear conductance as function of the bias voltage, we propose reliable results at finite magnetic field and finite temperature. Furthermore, we demonstrate the exponentially small scale of the Kondo temperature to appear in the second order derivative of the self-energy. We show that the approximation is, however, not able to reproduce the scaling of the effective mass at large interactions.