Ground State of the Parallel Double Quantum Dot System

We resolve the controversy regarding the ground state of the parallel double quantum dot system near half filling. The numerical renormalization group predicts an underscreened Kondo state with residual spin-$1/2$ magnetic moment, $\ln 2$ residual impurity entropy, and unitary conductance, while the Bethe ansatz solution predicts a fully screened impurity, regular Fermi-liquid ground state, and zero conductance. We calculate the impurity entropy of the system as a function of the temperature using the hybridization-expansion continuous-time quantum Monte Carlo technique, which is a numerically exact stochastic method, and find excellent agreement with the numerical renormalization group results. We show that the origin of the unconventional behavior in this model is the odd-symmetry “dark state” on the dots.

Figure 1

Schematic representation of the model for a parallel double quantum dot coupled to two semi-infinite tight-binding chains with equal hopping constants. The Fermi level is fixed at zero energy.

Figure 2

Comparison of the impurity entropy curves at the particle-hole symmetric point. Lines: NRG; circles: QMC results (with error bars). Energy unit is the half-bandwidth $D=1$.

Figure 3

Comparison of the impurity entropy curves away from the particle-hole symmetric point. Lines: NRG; circles: QMC results (with error bars).

Figure 4

Phase diagram in the $(ϵ,U)$ plane obtained by using the NRG. The entropy curve at point A is shown in Fig. 2, while those at points B and C are compared in Fig. 3.