Rok Žitko

Energy resolution and discretization artifacts in the numerical renormalization group

We study the limits of the energy resolution that can be achieved in the calculations of spectral functions of quantum impurity models using the numerical renormalization group NRG technique with interleaving z averaging. We show that overbroadening errors can be largely eliminated, that higher-moment spectral sum rules are satisfied to a good accuracy, and that positions, heights and widths of spectral features are well reproduced; the NRG approximates very well the spectral-weight distribution. We find, however, that the discretization of the conduction-band continuum nevertheless introduces artifacts. We present a modified discretization scheme which removes the band-edge discretization artifacts of the conventional approach and significantly improves the convergence to the continuum → 1 limit. Sample calculations of spectral functions with high energy resolution are presented. We follow in detail the emergence of the Kondo resonance in the Anderson impurity model as the electron-electron repulsion is increased, and the emergence of the phononic side peaks and the crossover from the spin Kondo effect to the charge Kondo effect in the AndersonHolstein impurity model as the electron-phonon coupling is increased. We also compute the spectral function of the Hubbard model within the dynamical mean-field theory, confirming the presence of fine structure in the Hubbard bands.

Multiple-impurity Anderson model for quantum dots coupled in parallel

The system of several N quantum dots coupled in parallel to the same single-mode conduction channel can be modeled as a single-channel N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the N-impurity S =1/2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin S =N / 2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to N /2�1/2 due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the N-impurity Anderson model to the exact Bethe ansatz results of a S =N /2 SU2 Kondo system we show that at low-temperature the quantum dots can be described by the effective S =N / 2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities N. We demonstrate the robustness of the spin N / 2 ground state as well as of the associated S =N / 2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.

Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

We thank J. Paaske for his comments on the paper. Work was supported by MINECO (Spain) Grants No. FIS2011-23526, No. FIS2012-33521, and by the Kavli Institute for Theoretical Physics through NSF Grant No. PHY11-25915. R.Ž. acknowledges the support of the Slovenian Research Agency (ARRS) under Program P1-0044.

Fano-Kondo effect in side-coupled double quantum dots at finite temperatures and the importance of two-stage Kondo screening

We study the zero-bias conductance through the system of two quantum dots, one of which is embedded directly between the source and drain electrodes, while the second dot is side coupled to the first one through a tunneling junction. Modeling the system using the two impurity Anderson model, we compute the temperature dependence of the conductance in various parameter regimes using the numerical renormalization group. We consider the noninteracting case, where we study the extent of the departure from the conventional Fano resonance line shape at finite temperatures, and the case where the embedded and/or the side-coupled quantum dot is interacting, where we study the consequences of the coexistence of the Kondo and Fano effects. If the side-coupled dot is very weakly interacting, the occupancy changes by two when the on-site energy crosses the Fermi level and a Fano-resonance-like shape is observed. If the interaction on the side-coupled dot is sizeable, the occupancy changes only by one and a very different line-shape results, which is strongly and characteristically temperature dependent. These results suggest an intriguing alternative interpretation of the recent experimental results study of the transport properties of the side-coupled double quantum dot [Sasaki et al., Phys. Rev. Lett. 103, 266806 (2009)]: the observed Fano-like conductance antiresonance may, in fact, result from the two-stage Kondo effect in the regime where the experimental temperature is between the higher and the lower Kondo temperature.

Spin thermopower in interacting quantum dots

Using analytical arguments and the numerical renormalization group method we investigate the spin-thermopower of a quantum dot in a magnetic field. In the particle-hole symmetric situation the temperature difference applied across the dot drives a pure spin current without accompanying charge current. For temperatures and fields at or above the Kondo temperature, but of the same order of magnitude, the spin-Seebeck coefficient is large, of the order of k_B/e. Via a mapping, we relate the spin-Seebeck coefficient to the charge-Seebeck coefficient of a negative-U quantum dot where the corresponding result was recently reported by Andergassen et al. in Phys. Rev. B 84, 241107 (2011). For several regimes we provide simplified analytical expressions. In the Kondo regime, the dependence of the spin-Seebeck coefficient on the temperature and the magnetic field is explained in terms of the shift of the Kondo resonance due to the field and its broadening with the temperature and the field. We also consider the influence of breaking the particle-hole symmetry and show that a pure spin current can still be realized provided a suitable electric voltage is applied across the dot. Then, except for large asymmetries, the behavior of the spin-Seebeck coefficient remains similar to that found in the particle-hole symmetric point.

Kondo effect in triple quantum dots

Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations, and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from local-moment to molecular-orbital behavior is visible in the evolution of correlation functions as the interdot coupling is increased. Resulting Kondo phases are presented in a phase diagram which can be sampled by measuring the zero-bias conductance. We discuss the origin of the even-odd effects by comparing with the double quantum dot.

Properties of anisotropic magnetic impurities on surfaces

Using numerical renormalization-group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy

Quantum phase transitions in systems of parallel quantum dots

D{S}_{z}^{2}

Non-Drude universal scaling laws for the optical response of local Fermi liquids

terms; such models are appropriate to describe magnetic impurity atoms adsorbed on nonmagnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy

Splitting of the Kondo resonance in anisotropic magnetic impurities on surfaces

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