We summarize recent theoretical results of our group concerning the electronic states of the strongly correlated fermions at nonzero temperature. The state of almost localized fermions is discussed within a mean-field approach for auxiliary bosons, both in the narrow-band (Section 2) and in the hybridized band (Section 3) cases. This state represents a metallic state of correlated fermion systems (such as V{sub 2}O{sub 3}) below the Mott-Hubbard localization threshold. The Fermi liquid state does not describe properly the properties of narrow band electrons in the large Hubbard -- U limit beyond the localization threshold. Therefore, in Section 4 and 5 we introduce a phenomenological concept of statistical spin liquid which describes principal features of a crossover from a high-temperature superconductor to the Mott insulator for a two-dimensional system. It also reproduces the main features of the phase diagram for La{sub 2-x}Sr{sub x}CuO{sub 4} system, which is modelled by a planar structure.
An effective Hamiltonian with auxiliary bosons and auxiliary fermions is proposed to treat the Hubbard Hamiltonian with strong correlation. Auxiliary particles themselves can not describe any real excitations. In particular, the Bose condensation of auxiliary bosons never occurs, and auxiliary fermions have no Fermi surfaces. Real excitations are described by two kinds of pair-excitations of auxiliary particles, such as fermionic and bosonic pair-excitations. Superconductivity in the effective Hamiltonian is nothing but the condensation of Cooper pairs between fermionic pair-excitations, which are formed by the superexchange interaction mediated by auxiliary fermions. The proposed model of superconductivity is consistent with anisotropic-singlet superconductivity previously examined by the present author (Jpn. J. Appl. Phys. 26 (1987) L652.), which is based on the Fermi liquid theory of the Hubbard Hamiltonian.
Electronic states in the two-dimensional Hubbard model are studied in the doped paramagnetic states by use of the auxiliary boson approach. Four auxiliary bosons are introduced by means of the Hubbard-Stratonovich transformation within the functional integral treatment. These bosons correspond to one charge and three spin fluctuations. An effective model is formulated. Going beyond the boson fluctuations around the saddle point, the single-electron Green's function including one-loop self-energy effects of fermion-boson interaction is derived. The behavior of the fermion self-energy, spectral functions, and density of states are investigated for several values of the Coulomb interaction
U within the limit imposed by the Stoner criterion and also for small and moderate doping concentrations $\ensuremath{\delta}$. For small doping $(\ensuremath{\delta}=0.2)$, as
U approaches a value determined by the Stoner criterion, the spin-boson spectrum has a striking low-energy enhancement around $\mathbf{q}\ensuremath{\sim}2{\mathbf{k}}_{F}.$ This enhancement of the spin fluctuation causes a non-Fermi-liquid-like low-energy $\ensuremath{\omega}$ linear dependence in the imaginary part of the self-energy. Due to the self-energy effects, band splittings and a band narrowing are produced in the spectral functions. As a consequence of this, the density of states has pseudogap structures around the quasiparticle band with a narrow bandwidth on the Fermi energy. These features seem to be precursors of the metal-insulator (Mott-Hubbard) transition and they might be related to the spin-gap phenomena observed in high-
Tc materials. Our results for the density of states, the spectral function, and the band dispersions show qualitative agreement with the data of finite-size cluster simulations.
We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The
f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the
f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons,
Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare
f level, where heavy-fermion behavior can be observed. For large-enough
Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while
Ud enhances the quasiparticle mass when the filling is close to half filling.
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. 1 1
It is shown that strongly interacting Fermi systems, such as
3He, transition metals, and the heavy-fermion systems can be consistently described within the ``induced''-interaction Fermi-liquid formalism. The general limiting features of the model are considered. In agreement with the Gutzwiller (half-filled case) solution to the Hubbard model, there is a localization of excitations as
F0s and
F1s\ensuremath{\rightarrow}\ensuremath{\infty}. Some of the large
m∗ originate from a large ``dynamic'' mass, ${m}_{\ensuremath{\lambda}}$ for f electrons, which is then shown to be further increased by many-body effects. In disagreement with the Gutzwiller solution in the half-filled case, but in agreement with the less-than-half-filled case, the compression modulus goes to a finite value as
F0s,
F1s\ensuremath{\rightarrow}\ensuremath{\infty}, so that---in a jellium model---the Debye frequency
FTHETAD has a finite value. The implication of the spin-dependent parameter
F0a going to a finite limit are discussed. In particular, it is shown that ferromagnetic ordering cannot occur in the case of a short-ranged potential.