Real-time renormalization group and cutoff scales in nonequilibrium applied to an arbitrary quantum dot in the Coulomb blockade regime

TL;DR

This paper develops a real-time renormalization group approach to analyze nonequilibrium quantum dot transport, incorporating various cutoff scales and applying it to magnetic molecules and Kondo models to study conductance and noise.

Contribution

It introduces a self-consistent one-loop RG formalism that includes all relevant cutoff scales for nonequilibrium quantum dots, extending previous methods.

Findings

Relaxation and dephasing rates cut off the RG flow.

Differential conductance shows quantum phase transition tunable by anisotropy.

Dephasing rate influences noise spectral features.

Abstract

We apply the real-time renormalization group (RG) in nonequilibrium to an arbitrary quantum dot in the Coulomb blockade regime. Within one-loop RG-equations, we include self-consistently the kernel governing the dynamics of the reduced density matrix of the dot. As a result, we find that relaxation and dephasing rates generically cut off the RG flow. In addition, we include all other cutoff scales defined by temperature, energy excitations, frequency, and voltage. We apply the formalism to transport through single molecular magnets, realized by the fully anisotropic Kondo model (with three different exchange couplings J_x, J_y, and J_z) in a magnetic field h_z. We calculate the differential conductance as function of bias voltage V and discuss a quantum phase transition which can be tuned by changing the sign of J_x J_y J_z via the anisotropy parameters. Finally, we calculate the noise S(Omega) at finite frequency Omega for the isotropic Kondo model and find that the dephasing rate determines the height of the shoulders in dS(\Omega)/d Omega near Omega=V.