The Hubbard Model at Infinite Dimensions: Thermodynamic and Transport Properties

We present results on thermodynamic quantities, resistivity and optical conductivity for the Hubbard model on a simple hypercubic lattice in infinite dimensions. Our results for the paramagnetic phase display the features expected from an intuitive analysis of the one-particle spectra and substantiate the similarity of the physics of the Hubbard model to those of heavy fermion systems. The calculations were performed using an approximate solution to the single-impurity Anderson model, which is the key quantity entering the solution of the Hubbard model in this limit. To establish the quality of this approximation we compare its results, together with those obtained from two other widely used methods, to essentially exact quantum Monte Carlo results.Comment: 29 pages, 16 figure

Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.Comment: 20 pages, 9 figures, accepted to PR

Calculations of the Knight Shift Anomalies in Heavy Electron Materials

We have studied the Knight shift $K(\vec r, T)$ and magnetic susceptibility $\chi(T)$ of heavy electron materials, modeled by the infinite U Anderson model with the NCA method. A systematic study of $K(\vec r, T)$ and $\chi(T)$ for different Kondo temperatures $T_0$ (which depends on the hybridization width $\Gamma$) shows a low temperature anomaly (nonlinear relation between $K$ and $\chi$) which increases as the Kondo temperature $T_0$ and distance $r$ increase. We carried out an incoherent lattice sum by adding the $K(\vec r)$ of a few hundred shells of rare earth atoms around a nucleus and compare the numerically calculated results with the experimental results. For CeSn_3, which is a concentrated heavy electron material, both the ^{119}Sn NMR Knight shift and positive muon Knight shift are studied. Also, lattice coherence effects by conduction electron scattering at every rare earth site are included using the average-T matrix approximation. Also NMR Knight shifts for YbCuAl and the proposed quadrupolar Kondo alloy Y_{0.8}U_{0.2}Pd_{3} are studied.Comment: 31 pages of RevTex, 22 Postscript figures, submmitted to PRB, some figures are delete

Numerical Renormalization Group Study of Pseudo-Fermion and Slave-Boson Spectral Functions in the Single Impurity Anderson Model

We use the numerical renormalization group to calculate the auxiliary spectral functions of the $U=\infty$ Anderson impurity model. The slave--boson and pseudo--fermion spectral functions diverge at the threshold with exponents $\alpha_{b}$ and $\alpha_{f}$ given in terms of the conduction electron phase shifts by the X--ray photoemission and the X--ray absorption exponents respectively. The exact exponents obtained here depend on the impurity occupation number, in contrast to the NCA results. Vertex corrections in the convolution formulae for physical Green's functions are singular at the threshold and may not be neglected in the Fermi liquid regime.Comment: 12 pages, RevTeX 3.0, 2 PS figures appende

Theory of One-Channel vs. Multi-Channel Kondo Effects for Ce3+^{3+} Impurities

We introduce a model for Ce$^{3+}$ impurities in cubic metals which exhibits competition between the Fermi-liquid fixed point of the single channel Kondo model and the non-Fermi-liquid fixed point of the two- and three-channel Kondo models. Using the non-crossing approximation and scaling theory, we find: (i) A possible three-channel Kondo effect between the one- and two-channel regimes in parameter space. (ii) The sign of the thermopower is a fixed point diagnostic. (iii) Our results will likely survive the introduction of additional $f^2$ and conduction states. We apply this model to interpret the non-Fermi liquid alloy La$_{1-x}$Ce$_x$Cu$_{2.2}$Si$_2$.Comment: 13 pages, Revtex, To appear in Phys. Rev. Let

Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.Comment: 5 pages, 1 figur

Phase Diagram of the Two-Channel Kondo Lattice

The phase diagram of the two-channel Kondo lattice model is examined with a Quantum Monte Carlo simulation in the limit of infinite dimensions. Commensurate (and incommensurate) antiferromagnetic and superconducting states are found. The antiferromagnetic transition is very weak and continuous; whereas the superconducting transition is discontinuous to an odd-frequency channel-singlet and spin-singlet pairing state.Comment: 5 pages, LaTeX and 4 PS figures (see also cond-mat/9609146 and cond-mat/9605109

Interannual variation patterns of total ozone and lower stratospheric temperature in observations and model simulations

We report results from a multiple linear regression analysis of long-term total ozone observations (1979 to 2000, by TOMS/SBUV), of temperature reanalyses (1958 to 2000, NCEP), and of two chemistry-climate model simulations (1960 to 1999, by ECHAM4.L39(DLR)/CHEM (=E39/C), and MAECHAM4-CHEM). The model runs are transient experiments, where observed sea surface temperatures, increasing source gas concentrations (CO2, CFCs, CH4, N2O, NOx), 11-year solar cycle, volcanic aerosols and the quasi-biennial oscillation (QBO) are all accounted for. MAECHAM4-CHEM covers the atmosphere from the surface up to 0.01 hPa ( 80 km). For a proper representation of middle atmosphere (MA) dynamics, it includes a parametrization for momentum deposition by dissipating gravity wave spectra. E39/C, on the other hand, has its top layer centered at 10 hPa ( 30 km). It is targeted on processes near the tropopause, and has more levels in this region. Despite some problems, both models generally reproduce the observed amplitudes and much of the observed lowlatitude patterns of the various modes of interannual variability in total ozone and lower stratospheric temperature. In most aspects MAECHAM4-CHEM performs slightly better than E39/C. MAECHAM4-CHEM overestimates the longterm decline of total ozone, whereas E39/C underestimates the decline over Antarctica and at northern mid-latitudes. The true long-term decline in winter and spring above the Correspondence to: W. Steinbrecht ([email protected]) Arctic may be underestimated by a lack of TOMS/SBUV observations in winter, particularly in the cold 1990s. Main contributions to the observed interannual variations of total ozone and lower stratospheric temperature at 50 hPa come from a linear trend (up to −10 DU/decade at high northern latitudes, up to −40 DU/decade at high southern latitudes, and around −0.7 K/decade over much of the globe), from the intensity of the polar vortices (more than 40 DU, or 8 K peak to peak), the QBO (up to 20 DU, or 2 K peak to peak), and from tropospheric weather (up to 20 DU, or 2 K peak to peak). Smaller variations are related to the 11-year solar cycle (generally less than 15 DU, or 1 K), or to ENSO (up to 10 DU, or 1 K). These observed variations are replicated well in the simulations. Volcanic eruptions have resulted in sporadic changes (up to −30 DU, or +3 K). At low latitudes, patterns are zonally symmetric. At higher latitudes, however, strong, zonally non-symmetric signals are found close to the Aleutian Islands or south of Australia. Such asymmetric features appear in the model runs as well, but often at different longitudes than in the observations. The results point to a key role of the zonally asymmetric Aleutian (or Australian) stratospheric anti-cyclones for interannual variations at high-latitudes, and for coupling between polar vortex strength, QBO, 11-year solar cycle and ENSO

Heavy-Fermions in LiV2O4: Kondo-Compensation vs. Spin-Liquid Behavior?

7Li NMR measurements were performed in the metallic spinel LiV2O4. The temperature dependencies of the line width, the Knight shift and the spin-lattice relaxation rate were investigated in the temperature range 30 mK < T < 280 K. For temperatures T < 1 K we observe a spin-lattice relaxation rate which slows down exponentially. The NMR results can be explained by a spin-liquid behavior and the opening of a spin gap of the order 0.6 K