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We investigate non-equilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures Marcus transfer rates are evaluated and at low temperatures, we calculate equilibrium and non-equilibrium population probabilities of the donor and acceptor with the non-perturbative Numerical Renormalization Group approach. We obtain the non-equilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend non-monotonically on the difference between the inter-site and on-site Coulomb interaction which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.

We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson's numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in the bands (governed by the band edges) and (iii) an arbitrary shape of the leads density of states. For a generic lead density of states the quantum dot favors being occupied by a particular spin-species due to exchange interaction with ferromagnetic leads leading to a suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry restoring the Kondo effect. We study both the gate-voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in presence of leads with an energy dependent density of states is not only possible by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given., Comment: 18 pages, 18 figures, accepted for publication in PRB

Measurements of electron transfer rates as well as of charge transport characteristics in DNA produced a number of seemingly contradictory results, ranging from insulating behaviour to the suggestion that DNA is an efficient medium for charge transport. Among other factors, environmental effects appear to play a crucial role in determining the effectivity of charge propagation along the double helix. This chapter gives an overview over charge transfer theories and their implication for addressing the interaction of a molecular conductor with a dissipative environment. Further, we focus on possible applications of these approaches for charge transport through DNA-based molecular wires.

Dynamical mean-field theory (DMFT) is a non-perturbative technique for the investigation of correlated electron systems. Its combination with the local density approximation (LDA) has recently led to a material-specific computational scheme for the ab initio investigation of correlated electron materials. The set-up of this approach and its application to materials such as (Sr,Ca)VO_3, V_2O_3, and Cerium is discussed. The calculated spectra are compared with the spectroscopically measured electronic excitation spectra. The surprising similarity between the spectra of the single-impurity Anderson model and of correlated bulk materials is also addressed., Comment: 20 pages, 9 figures, invited paper for the JPSJ Special Issue "Kondo Effect - 40 Years after the Discovery"; final version, references added

The numerical renormalization group method is used to investigate zero temperature phase transitions in quantum impurity systems, in particular in the soft-gap Anderson model, where an impurity couples to a non-trivial fermionic bath. In this case, zero temperature phase transitions occur between two different phases whose fixed points can be built up of non-interacting single-particle states. However, the quantum critical point cannot be described by non-interacting fermionic or bosonic excitations., Comment: 2 pages, 3 figures, submitted to SCES'04

The effect of a gate voltage ($V_g$) on the spin-splitting of an electronic level in a quantum dot (QD) attached to ferromagnetic leads is studied in the Kondo regime using a generalized numerical renormalization group technique. We find that the $V_g$-dependence of the QD level spin-splitting strongly depends on the shape of the density of states (DOS). For one class of DOS shapes there is nearly no $V_g$-dependence, for another, $V_g$ can be used to control the magnitude and sign of the spin-splitting, which can be interpreted as a local exchange magnetic field. We find that the spin-splitting acquires a new type of logarithmic divergence. We give an analytical explanation for our numerical results and explain how they arise due to spin-dependent charge fluctuations., Comment: 4 pages, 2 figures

The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the one-band Hubbard model has long been used to describe similar features in real materials like V$_2$O$_3$. Here we show that this transition is hidden inside a rather robust antiferromagnetic insulator even in the presence of comparatively strong magnetic frustration. This result raises the question of the relevance of the Mott-Hubbard metal-insulator transition for the generic phase diagram of the one-band Hubbard model., Comment: 4 pages, 6 figures

Inelastic light scattering from electrons is a symmetry-selective probe of the charge dynamics within correlated materials. Many measurements have been made on correlated insulators, and recent exact solutions in large dimensions explain a number of anomalous features found in experiments. Here we focus on the correlated metal, as described by the Hubbard model away from half filling. We can determine the B1g Raman response and the inelastic X-ray scattering along the Brillouin zone diagonal exactly in the large dimensional limit. We find a number of interesting features in the light scattering response which should be able to be seen in correlated metals such as the heavy fermions., Comment: 9 pages, 7 figures, typeset with ReVTeX

Zero temperature phase transitions not only occur in the bulk of quantum systems, but also at boundaries or impurities. We review recent work on quantum phase transitions in impurity models that are generalizations of the standard Kondo model describing the interaction of a localized magnetic moment with a metallic fermionic host. Whereas in the standard case the moment is screened for any antiferromagnetic Kondo coupling as T to 0, the common feature of all systems considered here is that Kondo screening is suppressed due to the competition with other processes. This competition can generate unstable fixed points associated with phase transitions, where the impurity properties undergo qualitative changes. In particular, we discuss the coupling to both non-trivial fermionic and bosonic baths as well as two-impurity models, and make connections to recent experiments., Comment: 9 pages, 3 figures, submitted to proceedings of 2nd Hvar workshop on Strongly Correlated Electrons

Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard model are studied by means of a generalization of the linearized dynamical mean-field theory. The method allows for an efficient and reliable determination of the critical interaction U_c for any integer filling n and different M at zero temperature. For half-filling a linear dependence of U_c on M is found. Inclusion of the (full) Hund's rule exchange J results in a strong reduction of U_c. The transition turns out to change qualitatively from continuous for J=0 to discontinuous for any finite J.

We investigate electron-phonon coupling in many-electron systems using dynamical mean-field theory in combination with the numerical renormalization group. This non-perturbative 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.

We report photoemission studies of polycrystalline samples of Sr-doped GdTiO_{3+delta}, which undergoes a Mott-Hubbard-like metal-insulator transition at a Ti-concentration of about 20%. The Ti 3d-derived valence band near the Fermi level displays a two-peak structure consistent with a Hubbard-model-type interpretation as quasiparticle and lower Hubbard band. Contrary to the theoretical expectation the lower Hubbard band does not change its energy with doping. However, the analysis of the core level spectra and elemental mapping with a scanning electron microscope indicate a strongly inhomogeneous doping concentration in the probed surface regions. This questions the intrinsic character of the valence band spectra and demonstrates a general difficulty when using polycrystalline samples for such studies.

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilise a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed., Comment: 9 pages, 11 figures

The numerically exact solution for nonresonant B1g Raman scattering is presented for the half-filled Hubbard model in infinite dimensions. This solution illustrates the modifications of the Raman response (in a system tuned through the quantum-critical point of a metal-insulator transition) due to Fermi-liquid properties in the metallic phase. In the insulating phase, we recover the predicted universal behavior, while we find the Raman response is quite anomalous on the metallic side of the transition. Our calculated results are similar to those measured in FeSi, SmB6, and underdoped cuprates., Comment: 5 pages, 4 figures, ReVTeX

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for $U$ larger than a critical value $U_c$, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping., Comment: 13 pages, 3 figures

Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for TT_c there is a smooth crossover from metallic-like to insulating-like solutions., Comment: 10 pages, 9 eps-figures

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the $d$-orbital, the charge-transfer energy between the $d$- and $p$-orbitals and the hopping integrals between $p-d$, $d-d$ and $p-p$ orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method., Comment: 10 pages, 4 figures

We show analytically that, under certain assumptions, the periodic Anderson model and the Hubbard model become equivalent within the dynamical mean field theory for quasiparticle weight Z -> 0. A scaling relation is derived which is validated numerically using the numerical renormalization group at zero temperature and quantum Monte Carlo simulations at finite temperatures. Our results show that the f-electrons of the half-filled periodic Anderson model with nearest neighbor hybridization get localized at a finite critical interaction strength U_c}, also at zero temperature. This transition is equivalent to the Mott-transition in the Hubbard model., Comment: 4 pages; accepted for publication in EPJ B

The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular the results for the Mott metal-insulator transition at low temperatures., Comment: 14 pages, 7 eps-figures included

Wilson's Numerical Renormalization Group method is used to study the paramagnetic ground state of the periodic Anderson model within the dynamical mean-field approach. For the particle-hole symmetric model, which is a Kondo insulator, we find that the lattice Kondo scale T_0 is strongly enhanced over the impurity scale T_K; T_0/T_K ~ exp(1/3I), where I is the Schrieffer-Wolff exchange coupling. In the metallic regime, where the conduction band filling is reduced from one, we find characteristic signatures of Nozi\`eres exhaustion scenario, including a strongly reduced lattice Kondo scale, a significant suppression of the states available to screen the f-electron moment, and a Kondo resonance with a strongly enhanced height. However, in contrast to the quantitative predictions of Nozi\`eres, we find that the T_0 ~ T_K with a coefficient which depends strongly on conduction band filling., Comment: 11 pages, 9 figures, submitted to Phys. Rev. B

We investigate the physics of a magnetic impurity with spin 1/2 in a correlated metallic host. Describing the band by a Hubbard Hamiltonian, the problem is analyzed using dynamical mean-field-theory in combination with Wilson's nonperturbative numerical renormalization group. We present results for the single-particle density of states and the dynamical spin susceptibility at zero temperature. New spectral features (side peaks) are found which should be observable experimentally. In addition, we find a general enhancement of the Kondo scale due to correlations. Nevertheless, in the metallic phase, the Kondo scale always vanishes exponentially in the limit of small hybridization., Comment: Final version, 4 pages RevTeX, 8 eps figures included

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. B

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion U_{\rm c} can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The ``linearized DMFT'' yields plausible results for the complete geometry dependence of the critical interaction., Comment: 8 pages

The zero temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the Dynamical Mean Field Theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's Numerical Renormalization Group method. Results for quasiparticle weight, spectral function and self-energy are discussed for Bethe and hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance which appears to be isolated from the Hubbard bands., Comment: 4 pages, 3 eps-figures included

We study the extended Hubbard model with both on-site and nearest neighbor Coulomb repulsion ($U$ and $V$, respectively) in the Dynamical Mean Field theory. At quarter filling, the model shows a transition to a charge ordered phase with different sublattice occupancies $n_A \nen_B$. The effective mass increases drastically at the critical $V$ and a pseudo-gap opens in the single-particle spectral function for higher values of $V$. The $V_c(T)$-curve has a negative slope for small temperatures, i.e. the charge ordering transition can be driven by increasing the temperature. This is due to the higher spin-entropy of the charge ordered phase., Comment: 4 pages, 4 EPS figures included, REVTeX

We present a new method to calculate directly the one-particle self-energy of an impurity Anderson model with Wilson's numerical Renormalization Group method by writing this quantity as the ratio of two correlation functions. This way of calculating Sigma(z) turns out to be considerably more reliable and accurate than via the impurity Green's function alone. We show results for the self-energy for the case of a constant coupling between impurity and conduction band (ImDelta = const) and the effective Delta(z) arising in the Dynamical Mean Field Theory of the Hubbard model. Implications to the problem of the metal-insulator transition in the Hubbard model are also discussed., Comment: 18 pages, 9 figures, submitted to J. Phys.: Condens. Matter

We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as rho(omega) \propto |omega|^r 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 powerlaw behaviour with different exponents in strong-coupling and local-moment regime. We also calculate the impurity spectral function which diverges (vanishes) with |omega|^{-r} (|\omega|^r) in the strong-coupling (local moment) regime., Comment: 8 pages, LaTeX, 4 figures includes as eps-files

We show that a Majorana fermion description of the two channel Kondo model can emerge quite naturally as a representation of the algebra associated with the spin currents in the two channels. Using this representation we derive an exact equivalent Hamiltonian for the two channel model expressed entirely in terms of Majorana fermions. The part of the Hamiltonian that is coupled to the impurity spin corresponds to the vector part of the $\sigma$-$\tau$ model (compactified two channel model). Consequently all the thermodynamic properties associated with the impurity spin can be calculated from the $\sigma$-$\tau$ model alone. The equivalent model can be used to confirm the interpretation of the many-body excitation spectrum of the low energy fixed point of the two-channel model as due to free Majorana fermions with appropriate boundary conditions., Comment: 4 pages, revtex, no figures

We study the single channel (compactified) models, the sigma-tau model and the O(3) symmetric Anderson model, which were introduced by Coleman et al., and Coleman and Schofield, as a simplified way to understand the low energy behaviour of the isotropic and anisotropic two channel Kondo systems. These models display both Fermi liquid and marginal Fermi liquid behaviour and an understanding of the nature of their low energy fixed points may give some general insights into the low energy behaviour of other strongly correlated systems. We calculate the excitation spectrum at the non-Fermi liquid fixed point of the sigma-tau model using conformal field theory, and show that the results are in agreement with those obtained in recent numerical renormalization group (NRG) calculations. For the O(3) Anderson model we find further logarithmic corrections in the weak coupling perturbation expansion to those obtained in earlier calculations, such that the renormalized interaction term now becomes marginally stable rather than marginally unstable. We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak and strong coupling regimes and show that the chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations., Comment: 23 pages, LaTeX, 11 figures includes as eps-files, submitted to Phys. Rev. B

We use the numerical renormalization group method to study the O(3)-symmetric version of the impurity Anderson model of Coleman and Schofield. This model is of general interest because it displays both Fermi liquid and non-Fermi liquid behaviour, and in the large $U$ limit can be related to the compactified two channel Kondo model of Coleman, Ioffe and Tsvelik. We calculate the thermodynamics for a parameter range which covers the full range of behaviour of the model. We find a non-Fermi liquid fixed point in the isotropic case which is unstable with respect to channel anisotropy., Comment: 10 pages, LaTeX, 8 figures includes as eps-files

Recently, a functional integral representation was proposed by Weller (Weller, W.: phys.~stat.~sol.~(b) {\bf 162}, 251 (1990)), in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This is achieved by introducing spin dependent Bose fields. The functional integral method is applied to the single impurity Anderson model both in the Kondo and mixed-valence regime. The f-electron Green's function and susceptibility are calculated using an Ising-like representation for the Bose fields. We discuss the difficulty to extract a spectral function from the knowledge of the imaginary time Green's function. The results are compared with NCA calculations., Comment: 11 pages, LaTeX, figures upon request, preprint No. 93/10/1