Dynamical Mean-Field Theory - from Quantum Impurity Physics to Lattice Problems

Since the first investigation of the Hubbard model in the limit of infinite dimensions by Metzner and Vollhardt, dynamical mean-field theory (DMFT) has become a very powerful tool for the investigation of lattice models of correlated electrons. In DMFT the lattice model is mapped on an effective quantum impurity model in a bath which has to be determined self-consistently. This approach lead to a significant progress in our understanding of typical correlation problems such as the Mott transition; furthermore, the combination of DMFT with ab-initio methods now allows for a realistic treatment of correlated materials. The focus of these lecture notes is on the relation between quantum impurity physics and the physics of lattice models within DMFT. Issues such as the observability of impurity quantum phase transitions in the corresponding lattice models are discussed in detail.Comment: 18 pages, 5 figures, invited paper for the Proceedings of the "3rd International Summer School on Strongly Correlated Systems, Debrecen, 2004

Pectinophora gossypiella (pink bollworm) Bacillus thuringiensis toxin receptor BT-R2

A cDNA encoding a 200 kD receptor, BT-R2, from the pink boll worm, Pectinophora gossypiella, that binds specifically to a Bacillus thuringiensis toxin has been cloned, sequenced and characterized. The minimum toxin binding fragment has been identified. The BT-R2 cDNA permits the analysis of receptors in pink boll worm and other insects that affect crop growth and development, as well as, design assays for the cytotoxicity and binding affinity of potential pesticides. The clone and other methods described herein, permit the manipulation of natural and/or introduced homologous receptors and, thus, to specifically destroy organisms, tissues and/or cells of the target host.Board of Regents, University of Texas Syste

Numerical Renormalization Group for Impurity Quantum Phase Transitions: Structure of Critical Fixed Points

The numerical renormalization group method is used to investigate zero temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.Comment: 14 pages, 12 figure

Numerical renormalization group study of the symmetric Anderson-Holstein model: phonon and electron spectral functions

We study the symmetric Anderson-Holstein (AH) model at zero temperature with Wilson's numerical renormalization group (NRG) technique to study the interplay between the electron-electron and electron-phonon interactions. An improved method for calculating the phonon propagator using the NRG technique is presented, which turns out to be more accurate and reliable than the previous works in that it calculates the phonon renormalization explicitly and satisfies the boson sum rule better. The method is applied to calculate the renormalized phonon propagators along with the electron propagators as the onsite Coulomb repulsion $U$ and electron-phonon coupling constant $g$ are varied. As $g$ is increased, the phonon mode is successively renormalized, and for $g \gtrsim g_{co}$ crosses over to the regime where the mode splits into two components, one of which approaches back to the bare frequency and the other develops into a soft mode. The initial renormalization of the phonon mode, as $g$ is increased from 0, depends on $U$ and the hybridization $\Delta$; it gets softened (hardened) for $U \gtrsim (\lesssim) U_s (\Delta)$. Correlated with the emergence of the soft mode is the central peak of the electron spectral function severely suppressed. These NRG calculations will be compared with the standard Green's function results for the weak coupling regime to understand the phonon renormalization and soft mode.Comment: 18 pages, 4 figures. Submitted to Phys. Rev.

Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model

We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general non-perturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at s=1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.Comment: 4 pages, 5 figs, (v2) final version as publishe

Spectral properties of locally correlated electrons in a BCS superconductor

We present a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. To this end the Anderson impurity model with superconducting bath is analysed by numerical renormalisation group (NRG) calculations. We calculate one and two-particle dynamic response function to elucidate the spectral excitation 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 also 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.Comment: 22 pages, 12 figure

Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model

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. Matte

Gap formation and soft phonon mode in the Holstein model

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