A. C. Hewson

Transport coefficients of the Anderson model via the numerical renormalization group

The transport coefficients of the Anderson model are calculated by extending Wilsons numerical renormalization group method to finite-temperature Green functions. Accurate results for the frequency and temperature dependence of the single-particle spectral densities and transport time tau ( omega , T) are obtained and used to extract the temperature dependence of the transport coefficients in the strong-correlation limit of the Anderson model. Results are obtained for values of the local level position ranging from the Kondo regime to the mixed valency and empty orbital regimes. The low-temperature anomalies in the resistivity, rho (T), thermopower, S(T), thermal conductivity, kappa (T), and Hall coefficient, RH(T), are discussed in terms of the behaviour of the spectral densities. At low temperature all quantities exhibit the expected Fermi liquid behaviour, rho (T)= rho 0(1-c(T/TK)2), S(T) approximately gamma T, kappa (T)/ alpha T=1+ beta (T/TK)2, RH(T)=-Rinfinity (1- delta (T/TK)2). Analytic results based on Fermi liquid theory are derived here for the first time for beta and the numerical results are shown to be consistent with this coefficient. The range of temperatures over which universal behaviour extends is also discussed. Scattering of conduction electrons in higher-angular-momentum, l>0, channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of the interference terms between the resonant l=0 and non-resonant l=1 channels on the transport properties. The presence of non-resonant scattering is shown to be particularly important for the thermopower at half filling, where the sign of the thermopower can depend sensitively on the non-resonant phase shift. Finally the relation of the results to experiment is discussed.

Numerical renormalization group calculations for the self-energy of the impurity Anderson model

We present a new method for calculating directly the one-particle self-energy of an impurity Anderson model with Wilsons numerical renormalization group method by writing this quantity as the ratio of two correlation functions. This way of calculating turns out to be considerably more reliable and accurate than that via the impurity Greens function alone. We give results for the self-energy for the case of a constant coupling between the impurity and the conduction band and the effective arising in the dynamical mean-field theory of the Hubbard model. The implications of the problem of the metal-insulator transition in the Hubbard model are also discussed.

Spectral properties of locally correlated electrons in a Bardeen–Cooper–Schrieffer superconductor

We present a detailed study of the spectral properties of a locally correlated site embedded in a Bardeen–Cooper–Schrieffer (BCS) superconducting medium. To this end the Anderson impurity model with a superconducting bath is analysed by means of numerical renormalization group calculations. We calculate one-and two-particle dynamic response functions to elucidate the spectral excitations and the nature of the ground state for different parameter regimes with and without particle–hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.

First- and second-order phase transitions in the Holstein-Hubbard model

We investigate metal-insulator transitions in the half-filled Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant, the transition is to a Mott insulator; when the electron-phonon interaction dominates, the transition is to a localized bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U. We also present results for the quasiparticle weight and the double occupancy as functions of U and g.

Numerical renormalization group study of the Anderson-Holstein impurity model

We present numerical renormalization group (NRG) calculations for a single-impurity Anderson model with a linear coupling to a local phonon mode. We calculate dynamical response functions, spectral densities, dynamic charge and spin susceptibilities. Being non-perturbative, the NRG is applicable for all parameter regimes. Our calculations cover both weak and strong electron-phonon coupling for zero and finite electron-electron interaction. We interpret the high- and low-energy features and compare our results to atomic limit calculations and perturbation theory. In certain restricted parameter regimes for strong electron-phonon coupling, a soft phonon mode develops inducing a very narrow resonance at the Fermi level.

Gap formation and soft phonon mode in the Holstein model.

We investigate electron-phonon coupling in many-electron systems using the dynamical mean-field theory in combination with the numerical renormalization group. This nonperturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions.

Anderson impurity in pseudo-gap Fermi systems

We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as with r > 0. We find two different fixed points: a local-moment fixed point with the impurity effectively decoupled from the band and a strong-coupling fixed point with a partially screened impurity spin. The specific heat and the spin susceptibility show power-law behaviour with different exponents in the strong-coupling and local-moment regimes. We also calculate the impurity spectral function which diverges (vanishes) with in the strong-coupling (local-moment) regime.

An exact limit of a local mixed valence model

Abstract Recently, Khomskii and Kocharjan have considered a local mixed valence model and, in a generalized linear Hartree-Fock approximation, found solutions which, when generalized to the many site problem, displayed continuous and discontinuous transitions from ground states of integral to intermediate valence. The transitions were due to an energy dependence of the virtual bound state width and persisted in the limit of zero hybridization. We examine the model of Khomskii and Kocharjan and demonstrate that in the limit of zero hybridization an exact solution may be found for the valence behaviour. The generalization of this result to the case of a small but finite concentration of localized level sites, exhibits intermediate valence only as a consequence of the pinning of the Fermi level to the narrow localized levels and the transitions between the ground states of integral and intermediate valence are continuous.

Kondo effects in a triangular triple quantum dot: Numerical renormalization group study in the whole region of the electron filling

We study the low-energy properties of a triangular triple quantum dot connected to two noninteracting leads in a wide parameter range, using the numerical renormalization group (NRG). Various kinds of Kondo effects take place in this system depending on the electron filling

Renormalized parameters for impurity models

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