Phase diagram and critical points of a double quantum dot

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 $T^{\ast }$ 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.

18 pages 31 figures

References in corpus (7)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Heavy Fermions and Quantum Phase Transitions
• Observation of the two-channel Kondo effect
• Quantum criticality in a double quantum-dot system
• Thermal and Electrical Transport across a Magnetic Quantum Critical Point
• Universal low-temperature crossover in two-channel Kondo models
• Renormalization group study of capacitively coupled double quantum dots

Cited by in corpus (11)

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• Magnetic field induced quantum criticality and the Luttinger sum rule
• Fate of the Kondo Effect and Impurity Quantum Phase Transitions Through the Lens of Fidelity Susceptibility
• Study of Hund's rule coupling in models of magnetic impurities and quantum dots
• Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
• Current cross-correlation in the Anderson impurity model with exchange interaction
• Qubit based on spin-singlet Yu-Shiba-Rusinov states
• Bell-state correlations in current of local Fermi liquid
• Fractional shot noise of an SU(N) Kondo system