Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo Models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.Comment: 26 pages, 18 figures, to be published in Eur. Phys. J.

Convergence acceleration and stabilization for dynamical-mean-field-theory calculations

The convergence to the self-consistency in the dynamical-mean-field-theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are used as the input to the impurity solver. It is shown that the techniques and the past experience with the mixing of input charge densities in the density-functional-theory (DFT) calculations are also effective in DMFT. As an example, the increase of the computational requirements near the Mott metal-insulator transition in the Hubbard model due to critical slowing down can be strongly reduced by using the modified Broyden's method to numerically solve the non-linear self-consistency equation. Speed-up factors as high as 3 were observed in practical calculations even for this relatively well behaved problem. Furthermore, the convergence can be achieved in difficult cases where simple linear mixing is either not effective or even leads to divergence. Unstable and metastable solutions can also be obtained. We also determine the linear response of the system with respect to the variations of the hybridization function, which is related to the propagation of the information between the different energy scales during the iteration.Comment: 9 pages, 8 figure

Mapping Itinerant Electrons around Kondo Impurities

We investigate single Fe and Co atoms buried below a Cu(100) surface using low temperature scanning tunneling spectroscopy. By mapping the local density of states of the itinerant electrons at the surface, the Kondo resonance near the Fermi energy is analyzed. Probing bulk impurities in this well-defined scattering geometry allows separating the physics of the Kondo system and the measuring process. The line shape of the Kondo signature shows an oscillatory behavior as a function of depth of the impurity as well as a function of lateral distance. The oscillation period along the different directions reveals that the spectral function of the itinerant electrons is anisotropic.Comment: 5 pages, 4 figures, accepted by Physical Review Letter

Slave-boson approach to the infinite-U Anderson-Holstein impurity model

The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility is renormalized. From the renormalized charge susceptibility the Kondo temperature is found to increase by the electron-phonon interaction. It turns out that the bosonic 1/N Gaussian fluctuations play a very crucial role, in particular, for the phonon propagator.Comment: 12pages, 3 figures. Published in Physical Review

The Fermi edge singularity in the SU(N) Wolff model

The low temperature properties of the SU(N) Wolff impurity model are studied via Abelian bosonization. The path integral treatment of the problem allows for an exact evaluation of low temperature properties of the model. The single particle Green's function enhances due to the presence of local correlation. The basic correlation function such as the charge or spin correlator are also influenced by the presence of impurity, and show local Fermi liquid behaviour. The X-ray absorption is affected by the presence of local Hubbard interaction. The exponent is decreased (increased) for repulsive (attractive) interactions.Comment: 7 pages, 4 figure

Resonating bipolarons

Electrons coupled to local lattice deformations end up in selftrapped localized molecular states involving their binding into bipolarons when the coupling is stronger than a certain critical value. Below that value they exist as essentially itinerant electrons. We propose that the abrupt crossover between the two regimes can be described by resonant pairing similar to the Feshbach resonance in binary atomic collision processes. Given the intrinsically local nature of the exchange of pairs of itinerant electrons and localized bipolarons, we demonstrate the occurrence of such a resonance on a finite-size cluster made out of metallic atoms surrounding a polaronic ligand center.Comment: 7 pages, 4 figures, to be published in Europhysics Letter

Non-equilibrium transport theory of the singlet-triplet transition: perturbative approach

We use a simple iterative perturbation theory to study the singlet-triplet (ST) transition in lateral and vertical quantum dots, modeled by the non-equilibrium two-level Anderson model. To a great surprise, the region of stable perturbation theory extends to relatively strong interactions, and this simple approach is able to reproduce all experimentally-observed features of the ST transition, including the formation of a dip in the differential conductance of a lateral dot indicative of the two-stage Kondo effect, or the maximum in the linear conductance around the transition point. Choosing the right starting point to the perturbation theory is, however, crucial to obtain reliable and meaningful results

Faithful fermionic representations of the Kondo lattice model

We study the Kondo lattice model using a class of canonical transformations that allow us to faithfully represent the model entirely in terms of fermions without constraints. The transformations generate interacting theories that we study using mean field theory. Of particular interest is a new manifestly O(3)-symmetric representation in terms of Majorana fermions at half-filling on bipartite lattices. This representation suggests a natural O(3)-symmetric trial state that is investigated and characterized as a gapped spin liquid.Comment: 11 pages, 2 figures, minor update

Conductance through an array of quantum dots

We propose a simple approach to study the conductance through an array of $N$ interacting quantum dots, weakly coupled to metallic leads. Using a mapping to an effective site which describes the low-lying excitations and a slave-boson representation in the saddle-point approximation, we calculated the conductance through the system. Explicit results are presented for N=1 and N=3: a linear array and an isosceles triangle. For N=1 in the Kondo limit, the results are in very good agreement with previous results obtained with numerical renormalization group (NRG). In the case of the linear trimer for odd $N$, when the parameters are such that electron-hole symmetry is induced, we obtain perfect conductance $G_0=2e^2/h$. The validity of the approach is discussed in detail.Comment: to appear in Phys. Rev.