For a mobile spin-1/2 impurity, coupled antiferromagnetically to a one-dimensional gas of fermions, perturbative ideas have been used to argue in favor of two-channel Kondo behavior of the impurity spin. Here we combine general considerations and ext
ensive numerical simulations to show that the problem displays a novel quantum phase transition between two-channel and one-channel Kondo screening upon increasing the Kondo coupling. We construct a ground-state phase diagram and discuss the various non-trivial crossovers as well as possible experimental realizations.
Coherent electronic transport through individual molecules is crucially sensitive to quantum interference. Using exact diagonalization techniques, we investigate the zero-bias and zero-temperature conductance through $pi$-conjugated annulene molecule
s (modeled by the Pariser-Parr-Pople and Hubbard Hamiltonians) weakly coupled to two leads. We analyze the conductance for different source-drain configurations, finding an important reduction for certain transmission channels and for particular geometries as a consequence of destructive quantum interference between states with definite momenta. When translational symmetry is broken by an external perturbation we find an abrupt increase of the conductance through those channels. Previous studies concentrated on the effect at the Fermi energy, where this effect is very small. By analysing the effect of symmetry breaking on the main transmission channels we find a much larger response thus leading to the possibility of a larger switching of the conductance through single molecules.
Using non-equilibrium renormalized perturbation theory, we calculate the conductance G as a function of temperature T and bias voltage V for an Anderson model, suitable for describing transport properties through a quantum dot. For renormalized param
eters that correspond to the extreme Kondo limit, we do not find a simple scaling formula beyond a quadratic dependence in T and V. However, if valence fluctuations are allowed, we find agreement with recent experiments.
We study the conductance through Aharonov-Bohm finite ladder rings with strongly interacting electrons, modelled by the prototypical t-J model. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic
flux, predicted so far only in chains which are a signature of spin and charge separation. These results open the possibility of observing this peculiar many-body phenomenon in anisotropic ladder systems and in real nanoscopic devices.
Due to their focalizing properties, elliptic quantum corrals present very interesting physical behaviors. In this work, we analyze static and dynamical properties of these systems. Results are presented for realistic values of the parameters, which m
ight be useful for comparison with experiments. We study noninteracting corrals and their response to several kinds of external perturbations, observing that, for realistic values of the Fermi level, the dynamics involves only a few number of excited states, making the system quite robust with respect to possible sources of decoherence. We also study the system in the presence of two S=1/2 impurities located at its foci, which interact with the electrons of the ellipse via a superexchange interaction J. This system is diagonalized numerically and properties such as the spin gap and spin-spin static and dynamical correlations are studied. We find that, for small J, both spins are locked in a singlet or triplet state, for even or odd filling, respectively, and its spin dynamics consists mainly of a single peak above the spin gap. In this limit, we can define an effective Heisenberg Hamiltonian to describe the low-energy properties. For larger J, more states are involved and the localized spins decorrelate in a manner similar to the Ruderman-Kittel-Kasuya-Yosida-Kondo transition for the two-impurity problem.
