Strong Electronic Correlations and Spin-Orbitl Coupling in a Three-Band Hubbard Model

Florian Gebhard, K. Bott, M. Scheidler +2 more

In this second of three articles on the optical absorption of electrons in a halffilled Peierls-distorted chain we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction U we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of band-width W, separated by the Hubbard interaction U. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum dependent but static ground state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spindegenerate. This corresponds to the Hubbard model at temperatures large compared to the spin exchange energy.

T. A. Kaplan

Richard T. Scalettar

Arun Kumar Maurya, Md. Tahir Hossain Sarder, Amal Medhi

Abstract We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsion U , while it becomes Mott insulating with Néel AF order at higher U . Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently large U . The FM state occurs irrespective of the value of Hund’s coupling J . The ferromagnetism at J = 0 can be explained by the Stoner mechanism while that for J > 0 is shown to arise from the superexchange process. At this band filling, the Hund’s coupling J is known to have the Janus-faced effect on electronic correlations where it enhances correlations at smaller U while reducing it at higher U . We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund’s coupling J reduces the effect of electronic correlations at all U .

Arisato Kawabata

Koichi Kusakabe, Hideo Aoki

The peculiar effect of electron correlation in multiband systems is illustrated for the recently proposed ferromagnetism in a Hubbard model having flat bands. Depsite the flatness of the band, an acoustic spin-wave mode with a finite stiffness exists along with optical modes below a Stoner gap. The relevant energy (gap and stiffness) transmutes from the Hubbard U in the weak-coupling limit to t (transfer integral) in the strong-coupling limit. This implies a stable itinerant ferromagnetism with finite band widths.