NRG approach to the transport through a finite Hubbard chain connected to reservoirs

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.Comment: One typo found in Eq.(3) in previous version has been correcte

Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction

We propose a minimal model for the Josephson current through a quantum dot in a Kondo regime. We start with the model that consists of an Anderson impurity connected to two superconducting (SC) leads with the gaps $\Delta_{\alpha}=|\Delta_{\alpha}| e^{i \theta_{\alpha}}$, where $\alpha = L, R$ for the lead at left and right. We show that, when one of the SC gaps is much larger than the others $|\Delta_L| \gg |\Delta_R|$, the starting model can be mapped exactly onto the single-channel model, which consists of the right lead of $\Delta_R$ and the Anderson impurity with an extra onsite SC gap of $\Delta_d \equiv \Gamma_L e^{i \theta_L}$. Here $\theta_L$ and $\Gamma_L$ are defined with respect to the starting model, and $\Gamma_L$ is the level width due to the coupling with the left lead. Based on this simplified model, we study the ground-state properties for the asymmetric gap, $|\Delta_L| \gg |\Delta_R|$, using the numerical renormalization group (NRG) method. The results show that the phase difference of the SC gaps $\phi \equiv \theta_R -\theta_L$, which induces the Josephson current, disturbs the screening of the local moment to destabilize the singlet ground state typical of the Kondo system. It can also drive the quantum phase transition to a magnetic doublet ground state, and at the critical point the Josephson current shows a discontinuous change. The asymmetry of the two SC gaps causes a re-entrant magnetic phase, in which the in-gap bound state lies close to the Fermi level.Comment: 23 pages, 13 figures, typos are correcte