We calculate the spin gap of homogeneous and inhomogeneous spin chains, using the White's density matrix renormalization group technique. We found that the spin gap is related to the ration between the spin velocity and the correlation exponent. We consider a spin superlattice, which is composed of a repeated pattern of two spin-¹/2 XXZ chains with different anisotropy parameters. The behavior of the charge velocity as a function of the anisotropy parameter and the relative size of sub-chains was investigated. We found reasonable agreement between the bosonization results and the numerical ones.

We study the scattering phase shift of the Kondo assisted transmission through a quantum dot (QD), considering a model that includes an additional non resonant channel transmission. To compute the phase evolution and the transmission amplitude of the QD, for different temperatures, we describe the QD employing the single Anderson impurity model in the limit of infinity Coulomb repulsion, within the X-boson approach. Our results are consistent with the development of an unusually large phase evolution at around pi in the Kondo valley, observed in recent experiments, and is consistent with others theoretical treatments.

We describe the Kondo resonance in quantum dots employing the atomic model. We calculate approximate Green's functions of the impurity Anderson model employing the exact solution of the system with a conduction band with zero width, and we use the completeness condition to choose the position of that band. At low temperatures, there are two solutions close to the chemical potential µ, satisfying this condition, and we choose the one with minimum Helmholtz free energy, considering that this corresponds to the Kondo solution. At high temperatures, this solution no longer exist, corresponding to the disappearance of the Kondo peak. We present curves of density of states that characterize the Kondo peak structure problem. As a simple application we calculate the conductance of a side-coupled quantum dot and we obtain good agreement with recent experimental results.

We are interested in studying the transport properties of metallic single-wall carbon nanotubes (SWCNTs) with isolated magnetic impurities. We consider a metallic zigzag SWCNT in the form of an infinitely long cylinder of diameter D, connected by two metallic electrodes under a bias voltage $E$, with a magnetic impurity located on its surface. To describe the Kondo resonance we employ an impurity version of the atomic model, previously developed to study the Kondo insulator properties in the lattice case. We calculate the approximate Green's functions of the impurity Anderson model by employing the exact solution of the atomic limit of the Anderson model, where we use the completeness condition to choose the position of the chemical potential. We consider the SWCNT Green's functions in a tight-binding approach. We calculate density of states curves that characterize well the structure of the Kondo peak and we also present the dependence of the conductance with the diameter of the SWCNT.