Thermodynamics of theSU(N) Anderson impurity

The thermodynamic Bethe-ansatz equations of the degenerate Anderson model are derived in theU» limit, where the multiple occupation of the localized level is excluded. The Kondo (Coqblin-Schrieffer) limit and the Fermi liquid behavior at lowT are extracted from these equations.     

Thermodynamics of theSU(N) anderson impurity

The thermodynamic Bethe-ansatz equations of the degenerate Anderson model in theU limit with excluded multiple occupation of the localized level are solved numerically for the casesN=2, 3, 4, and 6. The f-level occupation, the entropy, the spin and charge susceptibilities and the specific heat are obtained as a function of temperature for variousf-level energies.Heisenberg-fellow of the Deutsche Forschungsgemeinschaft     

Dimension of the commutant for theSU(N) affine algebras

Explicit formulae are obtained, giving the number of independent matrices which commute with the matricesS andT describing the modular transformations of theSU(N) affine characters.Chercheur IISN     

On the largeN c limit of theSU(N c ) colour quark-gluon partition function

Using Shifman-Vainshtein-Zakharov sum rules applied to three-point Green functions we obtain mass differences betweenSU _F (3) isomultiplets for the 1/2⁺ baryons. We also give some results for theg _A /g _V ratio.     

The neutralinos of theSU(N,1) minimal supergravity model and standard cosmology

We discuss the effect of the lightest supersymmetric particle (LSP), a Higgsino, and of the gravitino of theSU(N,1) minimal SUGRA model in the standard big bang theory. The freeze out of the LSP depends on the gravitino mass and on the top mass and leads to restrictive lower bounds for these parameters in the model. The decay of a gravitino with mass in the few TeV range leads to a delay in the cooling of the universe before nucleosynthesis. This constitutes the main bound on the gravitino mass of the model. The results are compared with the more standard “simultaneous decay approximation”.     

Quasi-confinement in theSU(3)-gluon plasma

We investigate a phenomenological equation of state for the gluon plasma, which differs from the ideal gluon gas equation of state in three aspects: (a) it is assumed that gluons withlow momentum are subject to confining interactions anddo not contribute to the energy spectrum of free gluons; (b)only gluons withhigh momentum are considered as an ideal gas with perturbative corrections of orderO(α_s); (c) a non-perturbative vacuum pressure is included. We show that feature (a) allows for a reasonable perturbative treatment of the interaction between gluons with high momentum. The equation of state reproduces lattice data for the thermodynamical functions of theSU(3) pure gauge theory above the deconfinement transition temperatureT _c. This result suggests that a possible way to describe the gluon plasma is in terms of perturbatively interacting gluons and non-perturbative “glueball” states.     

Ground state properties of the two impurity Anderson model in a 1/N expansion

The intersite contribution to the ground state energy for the two impurity Anderson model is calculated to first order in 1/N. The dependence of this contribution on the interimpurity separation has an R^?1 or R^?3 envelope for distances smaller or larger than a length ν_F/T_A ranges from a value equal to the bare ?-level position (in the weak valent regime) to the Kondo temperature (in the local moment limit).     

Anderson impurity in a correlated conduction band

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.     

One-dimensional multiband correlated conductors and Anderson impurity physics

A single Anderson impurity model recently predicted, through its unstable fixed point, the phase diagram of a two-band model correlated conductor, well confirmed by dynamical mean-field theory in infinite dimensions. We study here the one-dimensional version of the same model and extract its phase diagram in the opposite limit of reduced dimensionality. As expected for one dimension, the Mott metal-insulator transition at half filling is replaced by a dimerized insulator-undimerized Mott insulator transition, while away from half filling the strongly correlated superconductivity for inverted Hund's rule exchange in infinite dimensions is replaced by dominant pairing fluctuations. Many other aspects of the one-dimensional system, in particular, the field theories and their symmetries, are remarkably the same as those of the Anderson impurity, whose importance appears enhanced.     

Testing the rotational symmetry of theSU(3) potential

We test the static quark-antiquark potential inSU(3) lattice gauge theory, at β=5.8 on a 16⁴ lattice. We find an anisotropy on the level of 3% for small distances,r?3a. We discuss the implications of this effect on the determination of the string tension.     

Simple approximation scheme for the Anderson impurity Hamiltonian

A simple approximation scheme is presented for solving the Anderson impurity model within the Noncrossing Approximation (NCA). It is shown that with it the computations reduce to an extent that the scheme can be readily applied to interpret different experiments. The theory is applied to calculate the temperature dependence of the quadrupole moment and of the static and dynamic magnetic susceptibility. The effects of the crystalline electric field (CEF) are thereby incorporated. A comparison of the static susceptibility with exact Bethe ansatz results is given, when the effect of the CEF is neglected. Comparisons with the numerically exact solutions of the NCA are made where they are available. The application of the present theory to YbCu₂Si₂ is discussed.     

Finite dimensional representations of theSU(2)-current Lie algebra

We give a complete classification of the finite dimensional solutions for the Lie functional equations ofSU(2).     

Exact and approximate results for the Anderson impurity model

This paper provides exact and rigorous upper and lower bounds to the ground state energy of the Single Impurity Anderson Model in the limit of infiniteU. The upper bound approximates the ground state energy very well and the corresponding state may be used as a starting point for further investigations. The energy spectrum of the Single Impurity Anderson Model is calculated exactly for a special non-trivial model density of states describing the bare band electrons. All approaches introduced here are compared to this exact result and to other ground state energy calculations.     

Functional integral approach to the single impurity Anderson model

Recently, a functional integral representation was proposed by Weller [1], 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. Thef-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.     

Simple construction ofSU(3) representations using theSU(2) projection technique

SU(3) representations for theSU(3) SU(2) chain are constructed in a new way usingSU(2) projection operators. TheSU(3) D-functions, presented in new parametrizations, are expressed in terms ofSU(2) D-functions and 6j-symbols.Valuable discussions with Dr. J. Niederle are gratefully acknowledged.     

Non-leptonic weak charmed baryon decays in theSU(4) semidynamical scheme

We study here the Cabibbo enhanced charmed baryon decays in theSU(4) semidynamical model. The weak Hamiltonian 20″ + 15 + 45 + 45* can have the parity violating amplitude for charmed baryon decays. Decay width and α for some modes are also calculated.