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

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 → 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.

Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings

“…[32] somewhat improves the results of the standard fRG scheme with the sharp cutoff. The last term χ Λ σ in Eq.…”

“…(6) regulates (fermionic) infrared modes of the bare propagator. We use the Litim-type regulator [61] of the form [32] …”

“…To treat the effects of two particle interaction U , we use the one-particle irreducible (1PI) version of the fRG method [53], supplemented by the counterterm, recently introduced in Ref. [32], which allows for treatment of local moments. This method starts with considering the non-interacting propagator of quantum dot system, obtained by projection of the leads and taking the wideband limit [25,59,60], as a matrix in the quantum dot space [25],…”

“…In particular, in the simplest ring geometry of the system, consisting of two quantum dots coupled in parallel to two common leads, the appearance of the phase transition to the SFL state is related to the specific electron redistribution between the even and odd states. For the parallel quantum dot system with all hopping parameters between dots and leads equal, the SFL state has been studied by various methods [31,32] and was shown to appear due to the full decoupling of the odd state from the leads, which yields formation of the local magnetic moment in the system.…”

“…Although this method was adapted to study quantum dot systems, including fairly complex geometries, long time ago [17,24,25,58], only recently its modification, allowing to describe SFL state and providing a good agreement with the numerical renormalization group data for parallel quantum dot system up to the intermediate value of the interaction, was proposed [32].…”