Slave-boson mean-field theory of spin- and orbital-ordered states in the   degenerate Hubbard model
  The mean-field theory with the use of the slave-boson functional method is generalized to take account of the spin- and orbital-ordered state in the doubly degenerate Hubbard model. Some numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree-Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the antiferromagnetic orbital state is shown to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is {\it negative}. 
Hideo Hasegawa (Tokyo Gakugei Univ.)