1. Models of magnetic impurities 2. Resistivity calculations and the resistance minimum 3. The Kondo problem 4. Renormalization group 5. Fermi liquid theories 6. Exact solutions Bethe ansatz 7. N-fold degenerate models I 8. II 9. Theory experiment 10. Strongly correlated fermions Appendices.

The transport coefficients of the Anderson model are calculated by extending Wilson's numerical renormalization group method to finite-temperature Green functions. Accurate results for frequency and temperature dependence single-particle spectral densities time tau ( omega , T) obtained used extract in strong-correlation limit model. Results values local level position ranging from Kondo regime mixed valency empty orbital regimes. low-temperature anomalies resistivity, rho (T), thermopower,...

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

We present a detailed study of the spectral properties locally correlated site embedded in BCS superconducting medium. To this end Anderson impurity model with bath is analysed by numerical renormalisation group (NRG) calculations. calculate one and two-particle dynamic response function to elucidate excitation nature ground state for different parameter regimes without particle-hole symmetry. The position weight Andreev bound states given all relevant parameters. also phase diagrams...

A non-interacting local Fermi liquid theory applicable to Ce, Sm, Eu and Yb metallic intermediate valence materials is presented. The induced density of states a given rare earth ion taken as the Lorentzian appropriate for impurity, which justification tentatively discussed. degeneracy resonance that magnetic configuration ion. results are applied f occupation, susceptibility specific heat. relationship existing in literature between zero temperature linear coefficient heat follows exactly...

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

In recent years inelastic neutron scattering experiments have revealed marked variations in the temperature dependence of rotational tunnelling spectra molecular groups various local environments. A new theoretical approach is developed here to explain these results. microscopic model a rigid group, whose degree freedom coupled lattice modes, formulated terms standard basis operators for states uncoupled system. It shown that complete description spectrum can be found time-dependent...

The problem of determining the conditions for occurrence localized moments in dilute alloys on basis Anderson's model is re-examined. From a coupled set Green's-function equations an approximate solution found which includes electron correlation impurity levels and passes over to exact limiting case isolated impurity. Hartree-Fock theory obtained only if Coulomb repulsion $U$ relatively small. When large effects are important, magnetic states energy shift caused by impurity-band scattering...

An important contribution towards the well-known ionization of alkali atoms chemisorbed at low coverages on transition metal surfaces comes from upward shift in valence level due to image force. The Hartree-Fock approximation for this shift, which adatom electron cloud is assumed static, may differ by up a factor two that using result self-image energy an distance d surface given v=e2/4d. resolution problem depends lifetime orbital and dielectric response surface. A simple model Hamiltonian...

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

We give a procedure for renormalized perturbation expansion. It is demonstrated the Anderson impurity model, but has wide potential application. To zero order it describes Landau noninteracting quasiparticles. first in interaction U\ifmmode \tilde{}\else \~{}\fi{} gives exact thermodynamic results low temperatures, and to second ${\mathit{T}}^{2}$ coefficient resistivity. The approach not restricted Fermi liquid regime provides framework systematic corrections theory.

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

We consider a version of the symmetric Anderson impurity model (compactified) which has non-Fermi-liquid weak-coupling regime. find that in Majorana fermion representation perturbation theory can be conveniently developed terms Pfaffian determinants and we use this formalism to calculate free energy, self-energies, vertex functions. also derive expressions for local conduction-electron charge spin-dynamical susceptibilities self-energies In second-order theory, linear temperature dependence...

The authors give numerical results for the asymptotic form of magnetic isotherm M(H) at T=0 weak and strong fields j=3/2, 5/2 7/2 Coqblin-Schrieffer model (1969). These are derived from integral equations based on exact diagonalisation model. low-field indicate a clear change in qualitative behaviour with j. They all show positive initial curvature which increases j contrasts sharply standard Kondo j=1/2. In high leading terms an expansion log (g mu H/T1) have been calculated. From these...

From an exact calculation of the density states for one electron in Sherrington-von Molnar model s-f resonance coupled to a local optical phonon mode authors find conditions necessary polaronic reduction width resonance. With notation nu relaxation shift, Delta 0 zero coupling, omega frequency and W conduction band width, they range W> > very little obtain exp(- / 0) only if >W. This condition is too strong be satisfied intermediate-valence systems. However, not adequate description...

The local polaron problem in which a electronic resonance wide conduction band is coupled to phonon mode considered. Earlier work extended by more complete treatment of the case where finite Fermi level present important for intermediate valence materials. authors demonstrate variational and perturbational methods that there can be renormalisation width factor exp(-n), n number phonons cloud. They discuss conditions this occur particular establish importance closeness level. physical basis...

It is shown that no well-defined Fermi surface exists on the "metallic" side of Mott transition in Hubbard's theory. An alternative approach suggested.DOI:https://doi.org/10.1103/RevModPhys.40.810©1968 American Physical Society

We propose a minimal model for the Josephson current through quantum dot in Kondo regime. start with that consists of an Anderson impurity connected to two superconducting (SC) leads gaps $\Delta_{\alpha}=|\Delta_{\alpha}| e^{i \theta_{\alpha}}$, where $\alpha = L, R$ lead at left and right. show that, when one SC is much larger than others $|\Delta_L| \gg |\Delta_R|$, starting can be mapped exactly onto single-channel model, which right $\Delta_R$ extra onsite gap $\Delta_d \equiv \Gamma_L...

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

We give a comprehensive analysis of the singular dynamics and low-energy fixed point one-channel impurity s-d models with ferromagnetic underscreened antiferromagnetic couplings. use numerical renormalization group (NRG) to perform calculations at T=0. The spectral densities one-electron Green's functions t-matrices are found have very sharp cusps Fermi level (w=0), but do not diverge. approach is governed by terms proportional 1/ln^2(w/T_0) as w -> 0. scaled NRG energy levels show slow...

For pt.I see ibid., vol.15, p.3841 (1982). The problem of explaining the temperature dependence observed in inelastic neutron scattering spectrum rotational tunnelling systems was considered an earlier paper and based on a model which threefold molecular group hindering potential is coupled to phonon modes. An expression derived for function terms correlation functions standard basis operators uncoupled system. Here authors extends perturbational approach calculation these that developed...

We illustrate the renormalized perturbation expansion method by applying it to a single-impurity Anderson model. Previously, we have shown that this approach gives exact leading-order results for specific heat, spin and charge susceptibilities temperature dependence of resistivity model in Fermi-liquid regime, when carried out second order interaction Ũ. Here consider effects higher-order quasiparticle scattering calculate third-order contributions H3-term impurity magnetization symmetric...