2 research outputs found
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
, where for the lead at left and right. We show that, when one of the SC gaps is
much larger than the others , the starting model can
be mapped exactly onto the single-channel model, which consists of the right
lead of and the Anderson impurity with an extra onsite SC gap of
. Here and are
defined with respect to the starting model, and 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, , using the numerical renormalization group (NRG) method. The
results show that the phase difference of the SC gaps , 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