Slave-boson mean-field theory of the antiferromagnetic state in the doubly degenerate Hubbard model: The half-filled case

The antiferromagnetic ground state of the half-filled Hubbard model with the doubly degenerate orbital has been studied by using the slave-boson mean-field theory, which was previously proposed by the present author. Numerical calculations for the simple cubic model have shown that the metal-insulator transition does not take place except at the vanishing interaction point, in strong contrast with its paramagnetic solution. The energy gap in the density of states of the antiferromagnetic insulator is much reduced by the effect of electron correlation. The exchange interaction $J$ plays an important role in the antiferromagnetism: although for $J=0\mathrm{}$ the sublattice magnetic moment $m$ in our theory is fairly smaller than $m_{\mathrm{HFA}}$ obtained in the Hartree-Fock approximation, $m$ for $J/U>\mathrm{}0.2\mathrm{}$ ($U$ is the Coulomb interaction) is increased to become comparable to $m_{\mathrm{HFA}}.$ Surprisingly, the antiferromagnetic state is easily destroyed if a small, negative exchange interaction $(J/U<\mathrm{}-0.05)$ is introduced.