Single-band Hubbard Hamiltonian Research Articles

Electrical Conduction in Narrow Energy Bands

The electrical conductivity of the single-band Hubbard Hamiltonian is calculated by use of the Boltzmann-Transport-Equation. We lean on the antiferromagnetic approach to this Hamiltonian. We obtain a semiconductor with an energy gap due to the electronic correlations and a semiconductor to metal transition at the Néel temperature TN.

Electrical Conductivity in Narrow Energy Bands

The electrical conductivity for a system of electrons described by the single-band Hubbard Hamiltonian is studied. An expression for the electrical conductivity that is applicable in the narrow-band regime, i.e., the bandwidth $\ensuremath{\Delta}$, much smaller than intra-atomic Coulomb repulsion $I$ is derived. It is shown that the conductivity vanishes at $T=0$ to first order in $\frac{\ensuremath{\Delta}}{I}$ for one electron per atomic site. For the non-half-filled-band case, the degeneracy of the (atomic limit) ground-state wave function plays a crucial role in yielding a nonzero value for the conductivity. The theory is used to analyze the experimental data in Li-doped NiO. It is demonstrated how, as a consequence of this theory, the contribution to the conductivity from the narrow $3{d}^{8}$ band is suppressed in the total conductivity, contrary to an ordinary band-theory approach to the transport properties of this band.

Antiferromagnetism in Narrow-Band Solids

The single-band Hubbard Hamiltonian is examined in the limit of bandwidth much less than intraatomic Coulomb interaction of electrons. We make use of the canonical transformation and "spectral decomposition" of the electron creation operators proposed by Harris and Lange to write down a Green's function which describes electrons in the lower of the split bands of Hubbard's solution. The equation of motion is solved using the moment-conserving decoupling approximation of Tahir-Kheli and Jarrett. We find within our approximation that it is impossible to have an antiferromagnetic state for other than one electron per site. To remedy this defect of the single-band model, we investigate a simplified two-band model in the limit of intra-atomic Coulomb and exchange interaction much greater than the bandwidth, and find that antiferromagnetism is possible for the two nearly half-filled bands. We also discuss effects of the antiferromagnetic ordering on the conductivity in our simplified model and discuss applicability of the theory to real transition metals and transition-metal oxides.