We propose a novel statistical-mechanical approach to a system of strongly correlated electrons in a partially filled narrow band which reproduces rigorously the situation in the atomic limit. In this approach the doubly occupied configurations are excluded both in the real and in the reciprocal spaces. Employing this principle we calculate the thermodynamic properties of those electrons. The metallic state, corresponding to a partially-filled-band case, exhibits a Fermi-liquid--type behavior at low temperatures and transforms into a spin liquid at high temperatures. This feature of our results is reminiscent of the behavior in both magnetic metals and heavy-fermion systems. Additionally, the approach reproduces correctly the statistical properties of the system of localized moments in the limit of the half-filled band, corresponding to the Mott insulating phase. These results are not obtained if one starts from the Fermi-Dirac distribution for the quasiparticles. The last assertion is reinforced by an explicit derivation of a statistical distribution function for correlated electrons which reduces to the Fermi-Dirac distribution in the limit of weak interactions, as well as to the distribution for the spin liquid derived earlier in the limit of strong correlation between the particles.
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.
In this work, we apply the extremely correlated Fermi liquid (ECFL) theory into studying the
t-
t′-
J model in one and two dimensions. In 1-d, we combine ECFL and time-dependent density matrix renormalization group (tDMRG) method. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as aTomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation,i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven bystrong quantum fluctuations inherent in one dimension. In 2-d, low energy properties of the metallic state of the two-dimensional
t-
J model are presented for second neighbor hopping with hole-doping (
t′leq0) and electron-doping (
t′>0), with various superexchange energy
J. The density and temperature dependent spectral properties, resistivity and Hall response are calculated. The spectral features display high thermal sensitivity at modest T for density
ngeq0.8, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. Flipping the sign of
t′ or varying doping
delta changes the curvature of the resistivity versus T curves between convex and concave, consistent to experimental findings.