Functional renormalization group approach to the singlet-triplet transition in quantum dots

TL;DR

This paper develops a functional renormalization group method to analyze the zero-bias transport in quantum dots undergoing a singlet-triplet transition, providing efficient and accurate insights into their conductance properties.

Contribution

It introduces a FRG approach tailored for spin-dependent interactions in quantum dots, effectively capturing the transition behavior with minimal computational effort.

Findings

Accurately reproduces conductance near the singlet-triplet transition

Aligns well with numerical renormalization group results

Validates perturbative renormalization group predictions

Abstract

We present a functional renormalization group approach to the zero bias transport properties of a quantum dot with two different orbitals and in presence of Hund's coupling. Tuning the energy separation of the orbital states, the quantum dot can be driven through a singlet-triplet transition. Our approach, based on the approach by Karrasch {\em et al} which we apply to spin-dependent interactions, recovers the key characteristics of the quantum dot transport properties with very little numerical effort. We present results on the conductance in the vicinity of the transition and compare our results both with previous numerical renormalization group results and with predictions of the perturbative renormalization group.