We discuss specific features of quasiparticles in a strong applied magnetic field and near the Mott-Hubbard localization: the strong spin dependence of the de Haasvan Alphen oscillations, the maximum in the field dependence of the linear specific-heat coefficient, and metamagnetic behavior. These properties are obtained within the approach involving auxiliary (slave boson) fields that provides both the Gutzwiller band narrowing and a nonlinear molecular field. The simultaneous observation of all three properties provides a consistent set of predictions of the mean-field approach to the almost-localized Fermi liquid. The situation for heavy fermion system CeRu2Siz is briefly discussed.Almost-localized systems of strongly correlated fermions comprise Mott-Hubbard systems [e.g., pure and doped Vz03 (Ref. 1) or La, , Sr"Ti03(Ref. 2)], heavy-fermion systems [such as UPt3, URu2Si2, or CeRu2Si2 (Ref. 3)], liquid He close to solidification, and high-temperature superconducting materials near the antiferromagnetic insulating state [e.g., La2 "Sr"CuO&for x-0.05 (Ref. 5) and YBa2Cu306+"for x-0.3 -0.4]. The first three classes of materials are frequently considered as Fermi liquids of almost localized quasiparticles, i.e. , the liquids bordering on a state with localized magnetic moments. The Fermi-liquid nature of their electronic or atomic (in the case of He) statesshould not be taken for granted, since close to the localization, regarded as a well-defined phase transition, one may encounter a soliton or other non-Fermi-liquid types of singleparticle excitations. The purpose of this paper is to propose a consistent set of experimentally verifiable predictions that determine the specific behavior of an almost-localized Fermi liquid in an applied magnetic field, treated within a simple single-particle approach. The lifetime effects for tempera-tures T~O, as well as the detailed applications to heavyfermion systems, will be discussed separately.In systems close to the Mott-Hubbard localization the band energy of quasiparticles is small (the effective mass m* -+~) and almost compensated by the short-range repulsive interaction among the carriers. In effect, the system is very susceptible to much weaker perturbations such as the exchange interactions (which lead to a spin-density wave formation on the itinerant side, and to antiferromagnetism on the insulating side), thermal noise (causing the disruption of a coherent band motion and a formation of localized moments at elevated temperature ), and applied magnetic field. The main goal of this paper is to show that the applied magnetic field induces a set experimentally verifiable new effects, namely, (i) a spectacular spin dependence of the effective mass as exhibited, e.g. , in de Haasvan Alphen oscillations, (ii) quasimetamagnetic behavior for the nonhalf-filled band case, and (iii) a strong and nonmonotonic magnetic field dependence of the linear specific-heat coefficient y. These effects should appear concurrently at low temperature.

The hydrogen molecules H 2 and ( ) H 2 2 are analyzed with electronic correlations taken into account between the s 1 electrons in an exact manner. The optimal single-particle Slater orbitals are evaluated in the correlated state of H 2 by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron-ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for the × H 2 2 rectangular configuration, as well its ground state energy.Keywords: hydrogen molecules, electron-proton coupling for hydrogen molecule, electronic correlations for hydrogen molecule, intermolecular hopping and interaction parameters MotivationThe few-site models of correlated fermions play an important role in singling out, in an exact manner, the role of various local intra-and inter-site interactions against hopping (i.e., containing both covalent and the ionic factors) and thus, in establishing the optimal correlated state of fermions [1-8] on a local (nanoscopic) scale. The model has also been used to obtain a realistic analytic estimate of the hydrogen-molecule energies of the ground and the excited states in the correlated state [9]. For this purpose, we have developed the so-called EDABI method, which combines Exact Diagonalization in the Fock space with a concomitant Ab Initio determination of the single-particle basis in the Hilbert space. So far, the method has been implemented by taking only s 1 Slater orbitals, one per site [10]. The method contains no parameters; the only approximation made is taking a truncated single-particle basis (i.e., one Slater orbital per site) when constructing the field operator, that in turn is used to derive the starting Hamiltonian in the second-quantization representation. This Hamiltonian represents an extended Hubbard Hamiltonian, with all two-site interactions taken into account and the solution comprises not only the exact eigenvalues of the few-site Hamiltonian, but also at the same time an evaluation of the adjustable single-particle wave functions in the correlated state. Also, the calculated thermodynamic properties rigorously exemplify [12,11] the low-and highenergy scales, corresponding to spin and local charge fluctuations, respectively. The former represents the precursory magnetic-ordering effect whereas the latter represents local effects accompanying the Mott-Hubbard transition. In general, our approach follows the tradition of accounting for interelectronic correlations via the second-quantization procedure, with the adjustment of single-particle wave functions, contained in microscopic parameters of the startin...

We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made.

We consider a model Hamiltonian for a dimer of length a including all the electronic one-and twobody terms consistent with a single orbital per site, a free Einstein phonon term for a frequency Ω, and an electron-phonon coupling g0 of the Holstein type. The bare electronic interaction parameters were evaluated in terms of Wannier functions built from Gaussian atomic orbitals. An effective polaronic Hamiltonian was obtained by an unrestricted displaced-oscillator transformation, followed by evaluation of the phononic terms over a squeezed-phonon variational wave function. For the cases of quarter-filled and half-filled orbital, and over a range of dimer length values, the ground state for given g0 and Ω was identified by simultaneously and independently optimizing the orbital shape, the phonon displacement and the squeezing effect strength. As a varies, we generally find discontinuous changes of both electronic and phononic states, accompanied by an appreciable renormalization of the effective electronic interactions across the transitions, due to the equilibrium shape of the wave functions strongly depending on the phononic regime and on the type of ground state. 71.38.+i, 31.90.+s

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Received ( ) Revised ( )We evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, in both the adiabatic and extreme non-adiabatic limit, for a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape. We find largely different values of the coupling parameters in the two limits, as well as different expressions of the corresponding terms in the Hamiltonian. Depending on the distance between the dimer ions, some of the two-body couplings are comparable, or even larger than the one-body ones.