Charge Gap in the One-Dimensional Extended Hubbard Model at Quarter Filling

We propose a new combined approach of the exact diagonalization, the renormalization group and the Bethe ansatz for precise estimates of the charge gap $\Delta$ in the one-dimensional extended Hubbard model with the onsite and the nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $\Delta$ including the prefactor without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $\Delta$ is exponentially small, beyond usual renormalization group methods and/or finite size scaling approaches. The detailed results of $\Delta$ down to of order of $10^{-10}$ near the MIT are shown as contour lines on the $U$-$V$ plane.Comment: 4 pages, 4 figure

Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional UU-VV Model at Quarter filling

The one-dimensional extended Hubbard model with both the on-site $U$ and the nearest neighbor $V$ interactions at quarter filling is studied by using a novel finite size scaling. We diagonalize finite size systems numerically and calculate the Luttinger-liquid parameter $K_{\rho}$ which is substituted into the renormalization group equation as an initial condition. It leads $K_\rho$ in the infinite size system and the result agrees very well with the available exact result with $U=\infty$. This approach also yields the charge gap in the insulating state near the metal-insulator transition where the characteristic energy becomes exponentially small and the usual finite size scaling is not applicable.Comment: 7 pages, 8 figures,submitted to PR

First-principles Study of the RKKY Interaction and the Quadrupole Order in the Pr 1-2-20 systems PrT2Al20 (T=Ti, V)

Electronic states and quadrupole orders in the Pr 1-2-20 systems PrT2Al20 (T=Ti, V) are investigated on the basis of the first-principles calculations. The effective 196 orbital model is derived to reproduce the first-principles electronic structures of LaT2Al20 (T=Ti, V) without contribution from the Pr 4f electrons which are considered to be well localized and is employed to calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between quadrupole and octupole moments of the Pr ions. Within the random phase approximation for the RKKY Hamiltonian, the most divergent susceptibility is found to be the quadrupole one for the wave vector Q = (0,0,0) in the case of PrTi2Al20 while that for Q = (pi/a,0,pi/a) in the case of PrV2Al20 as consistent with experimental observations in the both cases which exhibit the ferro-quadrupole (FQ) and the antiferro-quadrupole (AFQ) orders, respectively. We also discuss the ordered states using the mean-field approximation and find that, in the case of PrTi2Al20, the 1st-order phase transition to the O20 FQ order with a tiny discontinuity takes place as predicted by the Landau theory. In the case of PrV2Al20, the system exhibits two distinct O22 AFQ orders, AFQ-I and AFQ-II, and shows subsequent two phase transitions, the 2nd-order one from normal to AFQ-I and the 1st-order one from AFQ-I to AFQ-II, that may be responsible for the double transitions observed by specific heat measurements.Comment: 6 pages, 6 figure

Phase diagram and dynamic response functions of the Holstein-Hubbard model

We present the phase diagram and dynamical correlation functions for the Holstein-Hubbard model at half filling and at zero temperature. The calculations are based on the Dynamical Mean Field Theory. The effective impurity model is solved using Exact Diagonalization and the Numerical Renormalization Group. Excluding long-range order, we find three different paramagnetic phases, metallic, bipolaronic and Mott insulating, depending on the Hubbard interaction U and the electron-phonon coupling g. We present the behaviour of the one-electron spectral functions and phonon spectra close to the metal insulator transitions.Comment: contribution to the SCES04 conferenc

Electronic State of Na_xCoO_2 Based on the Two Dimensional Triangular Lattice d-p Model

The electronic state in a CoO_2 plane of the layered cobalt oxides Na_{x}CoO_2 is investigated by using the 11 band d-p model on a two-dimensional triangular lattice, where the tight-binding parameters are determined so as to fit the LDA band structure. Effects of the Coulomb interaction at a Co site: the intra- and inter-orbital direct terms U and U', the exchange coupling J and the pair-transfer J', are treated within the Hartree-Fock approximation. We also consider the effect of the Na order at x=0.5, where Na ions form one dimensional chains, by taking into account of an effective one-dimensional potential Delta epsilon_{d} on the CoO_2 plane. It is found that the Na order enhances the Fermi surface nesting resulting in the antiferromagnetism (AFM) which is suppressed due to the frustration effect in the case without the Na order. When U and Delta epsilon_{d} are varied, we observe three types of the AFM: (1) the metallic AFM with large density of states N_F at the Fermi level for small values of U and Delta epsilon_{d}, (2) the semimetallic AFM with tiny N_F for large U with small Delta epsilon_{d} and (3) the insulating AFM with a finite energy gap for large values of U and Delta epsilon_{d}.Comment: 6 pages, 4 figure

Effect of the spin-orbit interaction and the electron phonon coupling on the electronic state in a silicon vacancy

The electronic state around a single vacancy in silicon crystal is investigated by using the Green's function approach. The triply degenerate charge states are found to be widely extended and account for extremely large elastic softening at low temperature as observed in recent ultrasonic experiments. When we include the LS coupling $\lambda_{\rm Si}$ on each Si atom, the 6-fold spin-orbital degeneracy for the $V^{+}$ state with the valence +1 and spin 1/2 splits into $\Gamma_{7}$ doublet groundstates and $\Gamma_{8}$ quartet excited states with a reduced excited energy of $O(\lambda_{\rm Si}/10)$. We also consider the effect of couplings between electrons and Jahn-Teller phonons in the dangling bonds within the second order perturbation and find that the groundstate becomes $\Gamma_{8}$ quartet which is responsible for the magnetic-field suppression of the softening in B-doped silicon.Comment: 4 pages, 2 figure

Mott transitions in correlated electron systems with orbital degrees of freedom

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

Crystalline-Electric-Field Effect on the Resistivity of Ce-based Heavy Fermion Systems

The behavior of the resistivity of Ce-based heavy fermion systems is studied using a 1/$N$-expansion method a la Nagoya, where $N$ is the spin-orbital degeneracy of f-electrons. The 1/$N$-expansion is performed in terms of the auxiliary particles, and a strict requirement of the local constraints is fulfilled for each order of 1/N. The physical quantities can be calculated over the entire temperature range by solving the coupled Dyson equations for the Green functions self-consistently at each temperature. This 1/N-expansion method is known to provide asymptotically exact results for the behavior of physical quantities in both low- and high-energy regions when it is applied to a single orbital periodic Anderson model (PAM). On the basis of a generalized PAM including crystalline-electric-field splitting with a single conduction band, the pressure dependence of the resistivity is calculated by parameterizing the effect of pressure as the variation of the hybridization parameter between the conduction electrons and f-electrons. The main result of the present study is that the double-peak structure of the $T$-dependence of the resistivity is shown to merge into a single-peak structure with increasing pressure.Comment: 37 pages, 22 figure

Field dependent effective masses in YbAl3_{3}

We show for the intermediate valence compound YbAl$_{3}$ that the high field (40 $\lesssim B \lesssim$ 60T) effective masses measured by the de Haas-van Alphen experiment for field along the $$ direction are smaller by approximately a factor of two than the low field masses. The field $B^{*} \sim$ 40T for this reduction is much smaller than the Kondo field $B_{K} \sim k_{B}T_{K}/\mu_{B}$ ($T_{K}\sim$ 670K) but is comparable to the field $k_{B}T_{coh}/\mu_{B}$ where $T_{coh}\sim$ 40K is the temperature for the onset of Fermi liquid coherence. This suggests that the field scale $B^{*}$ does not arise from 4$f$ polarization but is connected with the removal of the anomalies that are known to occur in the Fermi liquid state of this compound.Comment: 7 pages plus 3 figures Submitted to PRL 9/12/0

Periodic Anderson model with degenerate orbitals: linearized dynamical mean field theory approach

We investigate a multi-orbital extension of the periodic Anderson model with particular emphasis on electron correlations including orbital fluctuations. By means of a linearized version of the dynamical mean-field theory, we compute the renormalization factor, the density of states, the spectral gap and the local correlation functions for a given set of the intra- and inter-orbital Coulomb interactions as well as the Hund coupling. It is found that when a certain condition is met for the intra- and inter-orbital interactions for $f$ electrons, orbital fluctuations are enhanced, thereby enlarging the Kondo insulating gap. This effect is suppressed in the presence of the Hund coupling. We also clarify how the Kondo insulator is continuously changed to the Mott insulator when electron correlations among conduction electrons are increased.Comment: 7 pages, 10 figure