A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots

TL;DR

This paper introduces the functional renormalization group method for analyzing the Kondo effect in quantum dots, demonstrating its effectiveness in capturing key physical phenomena and its potential for studying complex quantum dot systems.

Contribution

It provides a practical implementation of the functional renormalization group for quantum dot transport, highlighting its ability to reproduce known results and extend to more complex setups.

Findings

Successfully captures the Kondo resonance and conductance plateau

Accurately reproduces the emergence of the Kondo scale

Demonstrates applicability to complex quantum dot configurations

Abstract

The functional renormalization group provides an efficient description of the interplay and competition of correlations on different energy scales in interacting Fermi systems. An exact hierarchy of flow equations yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Practical implementations rely on suitable truncations of the hierarchy, which capture nonuniversal properties at higher energy scales in addition to the universal low-energy asymptotics. As a specific example we study transport properties through a single-level quantum dot coupled to Fermi liquid leads. In particular, we focus on the temperature T=0 gate voltage dependence of the linear conductance. A comparison with exact results shows that the functional renormalization group approach captures the broad resonance plateau as well as the emergence of the Kondo scale. It can be easily extended to more complex setups of quantum dots.