Ground State of the Kondo-Hubbard Model at Half Filling

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 $J<\mathrm{}0\mathrm{}$ and $U>\mathrm{}|J|/4$ 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 $U>\mathrm{}|J|/4$, the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling $J_{\perp }>0\mathrm{}$ and $J_z\le 0$ for $U>\mathrm{}|J_z|/4$.