Phase diagram and critical points of a double quantum dot

TL;DR

This paper investigates the phase diagram and quantum critical points of a double quantum dot system using numerical and analytical methods, revealing a unified energy scale governing low-energy behavior and transitions.

Contribution

It combines NRG and RPT to analyze quantum critical points in a double quantum dot model, providing a comprehensive quantitative understanding of low-energy regimes.

Findings

Identification of two types of quantum critical points at J=J_c and U_{12}=U_{12}^c.

Confirmation that a single energy scale T^* governs low-energy behavior near critical points.

Applicability of results to broader classes of quantum critical systems, including heavy fermion materials.

Abstract

We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct interaction $U_{12}$ and an exchange interaction $J$. The model has two types of quantum critical points, one at $J=J_c$ to a local singlet state and one at $U_{12}=U_{12}^c$ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale $T^*$ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at $J=J_c$. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.