The ground state of the Hubbard model

Takashi Yanagisawa, Yukihiro Shimoi

We investigate the ground state of the Kondo-Hubbard model employing the recently introduced idea of spin-reflection positivity. It is shown exactly that the Kondo-Hubbard model for $J<0$ and $U>|J|/4$ at half filling has a unique ground state which can be ferromagnetic or singlet according to the lattice structure. In particular, for the Kondo lattice with $U>|J|/4$, the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling ${J}_{\ensuremath{\perp}}>0$ and ${J}_{z}\ensuremath{\le}0$ for $U>|{J}_{z}|/4$.

Assa Auerbach

Haiming Duan

By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.

Yoshihiro Asai

Andreas Mielke

A Hubbard model with a single, partially flat band has ferromagnetic ground states. It is shown that local stability of ferromagnetism implies its global stability in such a model: The model has only ferromagnetic ground states if there are no single spin-flip ground states. Since a single-band Hubbard model away from half filling describes a metal, this result may open a route to metallic ferromagnetism in single-band Hubbard models.

K. Dichtel, Rainer J. Jelitto, Heinz Koppe