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The magnetic properties of FeGe and FeSi are studied in a unified way on the basis of the realistic model derived from the first principle calculations. We can show that, with decreasing the temperature, the transition from the paramagnetic metallic state to the ferromagnetic metallic state takes place for FeGe, while the transition of FeSi from the paramagnetic metal to the paramagnetic insulator is a continuous crossover, consistent with experiments. It is shown that the distinct magnetic behaviors in FeGe and FeSi are attributed to the difference of the strength of the electron correlation effects, controlled by the effective bandwidth.

The Hall coefficient ${R}_{H}$ in high-${T}_{c}$ cuprates in the normal state shows the striking non-Fermi-liquid behavior: ${R}_{H}$ follows a Curie-Weiss type temperature dependence and $|{R}_{H}|\ensuremath{\gg}1/|\mathrm{ne}|$ at low temperatures in the underdoped compounds. Moreover, ${R}_{H}$ is positive for hole-doped compounds and negative for electron-doped ones, although each of them has a similar holelike Fermi surface. In this paper, we give the explanation of this long-standing problem from the standpoint of the nearly antiferromagnetic (AF) Fermi liquid. We consider seriously the vertex corrections for the current which are indispensable to satisfy the conservation laws, which are violated within the conventional Boltzmann transport approximation. The obtained total current ${J}_{\mathbf{k}}$ takes an enhanced value and is no longer perpendicular to the Fermi surface due to the strong AF fluctuations. By virtue of this mechanism, the anomalous behaviors of ${R}_{\mathrm{H}}$ in high-${\mathrm{T}}_{c}$ cuprates are naturally explained. Both the temperature and the (electron, hole) doping dependences of ${R}_{H}$ in high-${T}_{c}$ cuprates are reproduced well by numerical calculations based on the fluctuation-exchange approximation, applied to the single-band Hubbard model with a holelike Fermi surface. We also discuss the singular temperature dependence of ${R}_{\mathrm{H}}$ in other nearly AF metals, e.g., ${\mathrm{V}}_{2}{\mathrm{O}}_{3},$ $\ensuremath{\kappa}$-BEDT-TTF organic superconductors, and heavy fermion systems close to the AF phase boundary.

We study the metal-insulator transition accompanied with a charge ordering in the one-dimensional $t$-${J}^{\ensuremath{'}}$ model at quarter filling by the density-matrix renormalization-group method. In this model the nearest-neighbor hopping energy $t$ competes with the next-nearest-neighbor exchange energy ${J}^{\ensuremath{'}}$. We have found that a metal-insulator transition occurs at a finite value of ${t/J}^{\ensuremath{'}}$; ${(t/J}^{\ensuremath{'}}{)}_{C}\ensuremath{\simeq}0.18$ and the transition is of first order. In the insulating phase for small ${t/J}^{\ensuremath{'}}$, there is an alternating charge ordering and the system behaves as a one-dimensional quantum Heisenberg antiferromagnet. The metallic side belongs to the universality class of the Tomonaga-Luttinger liquids. The quantum phase transition is an example of melting of the one-dimensional quantum Heisenberg antiferromagnet.

Arguments are presented that in the one-dimensional Kondo lattice model f-electron spins participate in filling of the Fermi sea. It is shown that in its paramagnetic phase this model belongs to the spin-1/2 Tomonaga-Luttinger liquid universality class. The ratio of the spin and charge velocities v_s/v_c and K_c are estimated to be of the order of (T_K/E_F)^{1/2}., Comment: LaTeX file, 5 pages, 4 Postscript figures

Using a combination of analytical techniques and quantum Monte Carlo simulations we investigate the coupled spin-ladder system LaCuO{sub 2.5}. At a critical ratio of the interladder to intraladder coupling (J{sup {prime}}/J){sub c}{approx}0.11 we find a quantum phase transition between a Neel ordered and a disordered state. At criticality the uniform susceptibility behaves as {chi}(T)=aT{sup 2} with a universal prefactor. At intermediate temperatures the system crosses over to a {open_quotes}decoupled ladders regime{close_quotes} with pseudogap-type behavior, similar to uncoupled ladders. This can explain the gaplike experimental data for the magnetic susceptibility of LaCuO{sub 2.5} despite the presence of long-range Neel order. {copyright} {ital 1997} {ital The American Physical Society}

We investigate the magnetic and metal-insulator (M-I) phase diagram of the $\frac{1}{5}$-depleted square-lattice Hubbard model at $\frac{1}{4}$ filling by the mean-field approximation. There exist three magnetic phases of nonmagnetic (N), antiferromagnetic (AF), and ferromagnetic (F) types, each realized for the large intrasquare hopping ${t}_{1}$, intersquare hopping ${t}_{2}$, and Coulomb interaction $U$, respectively. Within each magnetic phase, the M-I transition of Lifshitz type emerges and, finally, six kinds of phases are identified in the $U\ensuremath{-}{t}_{1}/{t}_{2}$ plane. When ${t}_{1}={t}_{2}$, we find that the Dirac cone and nearly flat band around the $\ensuremath{\Gamma}$ point form the SU(3) multiplet. The SU(3) effective theory well describes the phase transitions between NI, paramagnetic-metal (PM), and AF phases. The NI and AFI phases are characterized by different Berry phases as in polyacetylene or graphene.

We propose a new type of magnetically disordered ground state for a frustrated quantum antiferromagnet. This disordered state is an array of spin singlets spontaneously formed on four spin plaquettes. Both perturbation results and bond-operator calculations show that this phase has lower energy than the columnar dimer state. Analysis of available numerical data on finite clusters also supports the conclusion that this state is realized at intermediate frustrations., 9 pages, ReVTEX, 2 PS-figures

We study the phase diagram of the heavy fermion superconductor UPt{sub 3} within a phenomenological model with two nearly degenerate order parameters corresponding to the {ital A}{sub 1} and {ital E}{sub 1} irreducible representations. A weak effect on superconductivity from the crystal lattice is also assumed. This assumption on one side provides an explanation for the closeness of two critical temperatures. On the other side it yields parameters of the Ginzburg-Landau functional which lead to a single superconducting transition when the order of critical temperatures changes with pressure. The experimental {ital H}-{ital T} diagram with a tetracritical point is reconstructed in the {ital AE} model. Vortex lattices are found for two orientations of the field. Restrictions imposed on the theory of the UPt{sub 3} phase diagram by experiments at pressures above critical and in a tilted magnetic field are also discussed. {copyright} {ital 1996 The American Physical Society.}

Spin and charge excitations in the one-dimensional periodic Anderson model at half filling are studied in the entire range of the Coulomb interaction U. It is confirmed by exact numerical diagonalization of up to eight sites that an excitation gap exists for any U. In the strong-coupling region, both the spin-excitation gap ${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}$ and charge-excitation gap ${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$ decrease with increasing U. A finite-size scaling shows that ${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}$ decreases exponentially as a function of U which is consistent with the spin gap in the Kondo-lattice model. The charge gap ${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$ decreases much more slowly than the spin gap. The ratio between the two gaps, R=${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$/${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}$, increases monotonically from unity and diverges in the strong-coupling limit: it appears to be a useful quantity for measuring the strength of electron correlation in a Kondo insulator.

The ground state of the one-dimensional Kondo lattice model is examined in the strong-coupling regime. An effective Hamiltonian is developed to describe low-energy processes. This leads to a ferromagnetic ground state in this regime for all conduction electron densities. The spin excitations are those of a squeezed spin chain with ferromagnetic Heisenberg exchange coupling. In addition there are quasiparticle excitations, which are discussed in detail only for the case of half filling.

By finite-size analysis of exact diagonalization the existence of a finite spin gap is confirmed for both antiferromagnetic and ferromagnetic coupling in the half-filled Kondo lattice model. For all finite values of antiferromagnetic coupling the system belongs to a class of coherent Kondo spin singlet, whereas for any finite ferromagnetic coupling it scales to a spin S=1 antiferromagnetic chain with a Haldane gap.

The electronic structure of the two-dimensional Penrose lattice is studied by numerical diagonalization of a tight-binding Hamiltonian for finite systems with up to 3571 sites. We have analyzed the smoothness of the energy spectrum and localization behavior of the wave functions by level statistics and a generalized participation ratio. The results show that the energy spectrum contains a singular part, and most of the wave functions are critical, i.e., neither extended nor localized. These behaviors of the electronic properties are discussed based on their quasiperiodic lattice structure.

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U < 0 using the density matrix renormalization group method as well as a perturbation theory. We find that the ground state is a charge density wave state with a long range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap which is the same as the four-particle excitation gap is a non-monotonic function of U, while the spin gap and others increase with increasing |U| and have linear asymptotic behaviors., 4 pages, 3 figures, submitted

In order to discuss superconductivity in orbital degenerate systems, a microscopic Hamiltonian is introduced. Based on the degenerate model, a strong-coupling theory of superconductivity is developed within the fluctuation exchange (FLEX) approximation where spin and orbital fluctuations, spectra of electron, and superconducting gap function are self-consistently determined. Applying the FLEX approximation to the orbital degenerate model, it is shown that the $d_{x^2-y^2}$-wave superconducting phase is induced by increasing the orbital splitting energy which leads to the development and suppression of the spin and orbital fluctuations, respectively. It is proposed that the orbital splitting energy is a controlling parameter changing from the paramagnetic to the antiferromagnetic phase with the $d_{x^2-y^2}$-wave superconducting phase in between., 4 figures, submitted to PRB

The theory of quantum transport through a dot under a finite bias voltage is developed using perturbation theory in the Keldysh formalism. It is found that the Kondo resonance splits into double peaks when the voltage exceeds the Kondo temperature, $eV>k_B T_K $, which leads to the appearance of a second peak in conductance, in addition to the zero-bias peak. The possible relevance of the new peak to the 0.7 conductance anomaly observed in quantum point contact is discussed., 5 pages, 6 figures, REVTeX4, Final version accepted for publication in Phys. Rev. B 2003. We decided to eliminate the result of U=8, and thus the old result should not be referred to

We present a scenario that the multicomponent fluctuations, especially those of the spin-orbital coupled modes, lead to the mass enhancement observed in ${\mathrm{LiV}}_{2}{\mathrm{O}}_{4}.$ This phenomenon is possible because all these modes are fluctuating due to the geometrical frustration. To illustrate this mechanism, the ${t}_{2g}$-orbital Hubbard model on the pyrochlore lattice is studied based on the random-phase approximation. We derive the generalized susceptibility in the SU(6) spin-orbital space and calculate the free energy by using a coupling-constant integration. The estimated specific heat coefficient is of the correct order of magnitude to explain the experiment.