Interaction induced local moments in parallel quantum dots within the functional renormalization group approach

TL;DR

This paper introduces a modified functional renormalization-group method to accurately describe the singular Fermi liquid phase and quantum phase transitions in parallel quantum dot systems, aligning well with numerical renormalization group results.

Contribution

The authors develop a novel fRG scheme incorporating Litim cutoff and magnetic field control, enabling the study of SFL phases and quantum phase transitions in quantum dot structures.

Findings

Successfully describes the SFL phase and quantum phase transition.

Shows sizable spin splitting in the SFL phase as magnetic field approaches zero.

Achieves good agreement with numerical renormalization group conductance results.

Abstract

We propose a version of functional renormalization-group (fRG) approach, which is, due to including Litim-type cutoff and switching off (or reducing) the magnetic field during fRG flow, capable describing singular Fermi liquid (SFL) phase, formed due to presence of local moments in quantum dot structures. The proposed scheme allows to describe the first-order quantum phase transition from "singular" to the "regular" paramagnetic phase with applied gate voltage to parallel quantum dots, symmetrically coupled to leads, and shows sizable spin splitting of electronic states in the SFL phase in the limit of vanishing magnetic field $H\rightarrow 0$; the calculated conductance shows good agreement with the results of the numerical renormalization group. Using the proposed fRG approach with the counterterm, we also show that for asymmetric coupling of the leads to the dots the SFL behavior similar to that for the symmetric case persists, but with occupation numbers, effective energy levels and conductance changing continuously through the quantum phase transition into SFL phase.