Using different techniques, and Fermi-liquid relationships, we calculate the variation with applied magnetic field (up to second order) of the zero-temperature equilibrium conductance through a quantum dot described by the impurity Anderson model. We focus on the strong-coupling limit $U \gg \Delta$ where $U$ is the Coulomb repulsion and $\Delta$ is half the resonant-level width, and consider several values of the dot level energy $E_d$, ranging from the Kondo regime $\epsilon_F-E_d \gg \Delta$ to the intermediate-valence regime $\epsilon_F-E_d \sim \Delta$, where $\epsilon_F$ is the Fermi energy. We have mainly used density-matrix renormalization group (DMRG) and numerical renormalization group (NRG) combined with renormalized perturbation theory (RPT). Results for the dot occupancy and magnetic susceptibility from DMRG and NRG+RPT are compared with the corresponding Bethe ansatz results for $U \rightarrow \infty$, showing an excellent agreement once $E_d$ is renormalized by a constant Haldane shift. For $U < 3 \Delta$ a simple perturbative approach in $U$ agrees very well with the other methods. The conductance decreases with applied magnetic field for dot occupancies $n_d \sim 1$ and increases for $n_d \sim 0.5$ or $n_d \sim 1.5$ regardless of the value of $U$. We also relate the energy scale for the magnetic-field dependence of the conductance with the width of low energy peak in the spectral density of the dot

By means of a projector operator formalism we study the ground state properties of the Anderson Impurity Hamiltonian. The non‐perturbative treatment of the model agrees with the previous one, obtained by Inagaki [Prog. Theor. Phys. 62, 1441 (1979)] by means of a perturbation expansion with respect the hybridization term. We go beyond the Inagaki's formalism to the next leading order. It provides a very accurate calculation of the energy spectrum in the total spin ST=0 sector and, in particular, the ground state energy in the whole parameter space. For a one body spinless system, the dependence of the ground state energy as a function of the impurity level obtained by this procedure remarkably agrees with analytical results. For the many body case the occupancy of the impurity as a function of the parameters is studied and it agrees with the corresponding one obtained by using the Bethe ansatz and the Numerical Renormalization Group solution of the Hamiltonian. The magnetization and susceptibility of the impurity is analyzed by studying the response of the system to an external magnetic field, from which it is possible to extract the Kondo temperature. The dependence of the Kondo scale with the parameters of the model is in excellent agreement with well‐known results.

We study the texture of helical currents in metallic planar strips in the presence of Rashba spinorbit coupling (RSOC) on the lattice at zero temperature. In the noninteracting case, and in the absence of external electromagnetic sources, we determine by exact numerical diagonalization of the single-particle Hamiltonian, the distribution across the strip section of these Rashba helical currents (RHC) as well as their sign oscillation, as a function of the RSOC strength, strip width, electron filling, and strip boundary conditions. Then, we study the effects of charge currents introduced into the system by an Aharonov-Bohm flux for the case of rings or by a voltage bias in the case of open strips. The former setup is studied by variational Monte Carlo, and the later, by the time-dependent density-matrix-renormalization group technique. Particularly for strips formed by two, three and four coupled chains, we show how these RHC vary in the presence of such induced charge current, and how their differences between spin-up and spin-down electron currents on each chain, help to explain the distribution across the strip of charge currents, both of the spin conserving and the spin flipping types. We also predict the appearance of polarized charge currents on each chain. Finally, we show that these Rashba helical currents and their derived features remain in the presence of an on-site Hubbard repulsion as long as the system remains metallic, at quarter filling, and even at half-filling where a Mott-Hubbard metal-insulator transition occurs for large Hubbard repulsion.

Tetragonal CuO (T-CuO) has attracted attention because of its structure similar to that of the cuprates. It has been recently proposed as a compound whose study can give an end to the long debate about the proper microscopic modeling for cuprates. In this work, we rigorously derive an effective one-band generalized t-J model for T-CuO, based on orthogonalized Zhang-Rice singlets, and make an estimative calculation of its parameters, based on previous ab initio calculations. By means of the self-consistent Born approximation, we then evaluate the spectral function and the quasiparticle dispersion for a single hole doped in antiferromagnetically ordered half filled T-CuO. Our predictions show very good agreement with angle-resolved photoemission spectra and with theoretical multiband results. We conclude that a generalized t-J model remains the minimal Hamiltonian for a correct description of single-hole dynamics in cuprates.

We study the role played by the magnetic frustration in the antiferromagnetic phase of the organic salt κ−(BEDT −T T F )2Cu[N (CN )2]Cl. Using the spatially anisotropic triangular Heisenberg model we analyze previous and new performed NMR experiments. We compute the 1/T1 relaxation time by means of the modified spin wave theory. The strong suppression of the nuclear relaxation time observed experimentally under varying pressure and magnetic field is qualitatively well reproduced by the model. Our results suggest the existence of a close relation between the effects of pressure and magnetic frustration.

A system of two interacting Cobalt atoms, at varying distances, has been studied in a recent Scanning Tunneling Microscope experiment by J. Bork et al., Nature Physics 7, 901 (2011). We propose a microscopic model that explains, for all the experimentally analyzed interatomic distances, the physics observed in these experiments. Our proposal is based on the two-impurity Anderson model, with the inclusion of a two-path geometry for charge transport. This many-body system is treated in the finite-U Slave Boson Mean Field Approximation and the Logarithmic-Discretization Embedded-Cluster Approximation. We physically characterize the different charge transport regimes of this system at various interatomic distances and show that, as in the experiments, the features observed in the transport properties depend on the presence of two impurities but also on the existence of two conducting channels for electron transport. We interpret the splitting observed in the conductance as the result of the hybridization of the two Kondo resonances associated to each impurity.

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Building an effective Hamiltonian utilizing a projector‐operator procedure, we derive an approximation based on a self‐consistent hybridization expansion to study the ground state properties of the Anderson impurity model. We applied the approximation to the general case of finite Coulomb repulsion U, extending previous work with the same formalism in the infinite‐U case. The ground state energy and their related zero temperature properties are accurately obtained in the case in which U is large enough, but still finite, as compared with the rest of energy scales involved in the model. The results for the valence of the impurity are compared with exact results that we obtain from equations derived using the Bethe ansatz and with a perturbative approach. The magnetization and magnetic susceptibility is also compared with Bethe ansatz results. In order to do this comparison, we also show how to regularize the Bethe ansatz integral equations necessary to calculate the impurity valence, for arbitrary values of the parameters.