Mott transitions in correlated electron systems with orbital degrees of freedom

Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard model are studied by means of a generalization of the linearized dynamical mean-field theory. The method allows for an efficient and reliable determination of the critical interaction U-c for any integer filling n and different M at zero temperature. For half filling a linear dependence of U-c on M is found. Inclusion of the (full) Hund's rule exchange J results in a strong reduction of U-c. The transition turns out to change qualitatively from continuous for J=0 to discontinuous for any finite J. This result is confirmed using the exact-diagonalization method for M=2.