Cumulant expansion of the periodic Anderson model in infinite dimension

The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion ($U=\infty$) is considered here for an hypercubic lattice of infinite dimension ($d=\infty$). The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of $d=\infty$, are shown to be also valid for the periodic Anderson model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical and General (1997

Electronic State and Magnetic Susceptibility in Orbitally Degenerate (J=5/2) Periodic Anderson Model

Magnetic susceptibility in a heavy fermion systemis composed of the Pauli term (\chi_P) and the Van-Vleck term (\chi_V). The latter comes from the interband excitation, where f-orbital degeneracy is essential. In this work, we study \chi_P and \chi_V in the orbitally degenerate (J=5/2) periodic Anderson model for both the metallic and insulating cases. The effect of the correlation between f-electrons is investigated using the self-consistent second-order perturbation theory. The main results are as follows. (i) Sixfold degenerate model: both \chi_P and \chi_V are enhanced by a factor of 1/z (z is the renormalization constant). (ii) Nondegenerate model: only \chi_P is enhanced by 1/z. Thus, orbital degeneracy is indispensable for enhancement of \chi_V. Moreover, orbital degeneracy reduces the Wilson ratio and stabilizes a nonmagnetic Fermi liquid state.Comment: 4 pages, revtex, to be published in J. Phys. Soc. Jpn. (No.8

Calculation of Optical Conductivity, Resistivity and Thermopower of Filled Skutterudite CeRu4_4Sb12_{12} based on a Realistic Tight-binding Model with Strong Correlation

The filled-skutterudite compound CeRu$_4$Sb$_{12}$ shows a pseudo-gap structure in the optical conductivity spectra similar to the Kondo insulators, but metallic behavior below 80 K. The resistivity shows a large peak at 80 K, and the Seebeck coefficient is positive and also shows a large peak at nearly the same temperature. In order to explain all these features, a simplified tight-binding model, which captures the essential features of the band calculation, is proposed. Using this model and introducing the correlation effect within the framework of the dynamical mean field approximation and the iterative perturbation theory, the temperature dependences of the optical conductivity, resistivity and the Seebeck coefficient are calculated, which can explain the experiments.Comment: 4 pages, 6 figure

Interplay of Spin-Orbit Interaction and Electron Correlation on the Van Vleck Susceptibility in Transition Metal Compounds

We have studied the effects of electron correlation on Van Vleck susceptibility ($\chi_{\rm{VV}}$) in transition metal compounds. A typical crossover behavior is found for the correlation effect on $\chi_{\rm{VV}}$ as sweeping spin-orbit interaction, $\lambda$. For a small $\lambda$, orbital fluctuation plays a dominant role in the correlation enhancement of $\chi_{\rm{VV}}$; however, the enhancement rate is rather small. In contrast, for an intermediate $\lambda$, $\chi_{\rm{VV}}$ shows a substantial increase, accompanied by the development of spin fluctuation. We will discuss the behavior of $\chi_{\rm{VV}}$ in association with the results of Knight-shift experiments on Sr$_2$RuO$_4$ and an anomalously large magnetic susceptibility observed for $5d$ Ir compounds.Comment: 5 pages, 3 figures, to appear in J. Phys. Soc. Jp

Optical conductivity of the Kondo insulator YbB_12: Gap formation and low-energy excitations

Optical reflectivity experiments have been conducted on single crystals of the Kondo insulator YbB_12 in order to obtain its optical conductivity, \sigma(\omega). Upon cooling below 70 K, a strong supression of \sigma(\omega) is seen in the far-infrared region, indicating the opening of an energy gap of ~ 25 meV. This gap development is coincident with a rapid decrease in the magnetic susceptibility, which shows that the gap opening has significant influence on magnetic properties. A narrow, asymmetric peak is observed at ~40 meV in \sigma(\omega), which is attributed to optical transitions between the Yb 4f-derived states across the gap. In addition, a broad peak is observed at ~0.25 eV. This peak is attributed to transitions between Yb 4f-derived states and p-d band, and is reminiscent of similar peaks previously observed for rare-earth hexaborides.Comment: 4 pages, 4 figure

Anomalous Metal-Insulator Transition in Filled Skutterudite CeOs4_4Sb12_{12}

Anomalous metal-insulator transition observed in filled skutterudite CeOs$_4$Sb$_{12}$ is investigated by constructing the effective tight-binding model with the Coulomb repulsion between f electrons. By using the mean field approximation, magnetic susceptibilities are calculated and the phase diagram is obtained. When the band structure has a semimetallic character with small electron and hole pockets at $\Gamma$ and H points, a spin density wave transition with the ordering vector $\mathbf{Q}=(1,0,0)$ occurs due to the nesting property of the Fermi surfaces. Magnetic field enhances this phase in accord with the experiments.Comment: 4 pages, 4 figure

Thermodynamics of doped Kondo insulator in one dimension: Finite Temperature DMRG Study

The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approach to the values obtained in the Tomonaga-Luttinger (TL) liquid ground state for several parameters. The crossover temperature to the TL liquid is a new energy scale determined by gapless excitations of the TL liquid. The transition from the metallic phase to the insulating phase is accompanied by the vanishing of the lower crossover temperature.Comment: 4 pages, 7 Postscript figures, REVTe

Conductance through Quantum Dots Studied by Finite Temperature DMRG

With the Finite temperature Density Matrix Renormalization Group method (FT-DMRG), we depeloped a method to calculate thermo-dynamical quantities and the conductance of a quantum dot system. Conductance is written by the local density of states on the dot. The density of states is calculated with the numerical analytic continuation from the thermal Green's function which is obtained directly from the FT-DMRG. Typical Kondo behaviors in the quantum dot system are observed conveniently by comparing the conductance with the magnetic and charge susceptibilities: Coulomb oscillation peaks and the unitarity limit. We discuss advantage of this method compared with others.Comment: 14 pages, 13 fiure

Finite temperature properties of the 2D Kondo lattice model

Using recently developed Lanczos technique we study finite-temperature properties of the 2D Kondo lattice model at various fillings of the conduction band. At half filling the quasiparticle gap governs physical properties of the chemical potential and the charge susceptibility at small temperatures. In the intermediate coupling regime quasiparticle gap scales approximately linearly with Kondo coupling. Temperature dependence of the spin susceptibility reveals the existence of two different temperature scales. A spin gap in the intermediate regime leads to exponential drop of the spin susceptibility at low temperatures. Unusual scaling of spin susceptibility is found for temperatures above 0.6 J. Charge susceptibility at finite doping reveals existence of heavy quasiparticles. A new low energy scale is found at finite doping.Comment: REVTeX, 7 pages, 7 figure

Phase Diagram of the Electron-Doped Cuprate Superconductors

We investigate the phase diagram of the electron-doped systems in high-Tc cuprates. We calculate the superconducting transition temperature Tc, the antiferromagnetic transition temperature TN, the NMR relaxation rate 1/T1 with the antiferromagnetic fluctuations in the fluctuation-exchange (FLEX) approximation and with the superconducting fluctuations in the self-consistent t-matrix approximation. Obtained phase diagram has common features as those in the hole-doped systems, including the antiferromagnetic state, the superconducting state and the spin gap phenomenon. Doping-dependences of TN, Tc and Tsg (spin gap temperature) are, however, different with those in the hole-doped systems. These differences are due to the intrinsic nature of the ingap states which are intimately related with the Zhang-Rice singlets in the hole-doped systems and are correlated d-electrons in the electron-doped systems, respectively, which has been shown in the d-p model.Comment: 4 pages, 3 figure