The Mott-Hubbard transition is studied for a Hubbard model with orbital degeneracy N , using a diffusion Monte Carlo method. Based on general arguments, we conjecture that the Mott-Hubbard transition takes place for U/W ∼ √ N , where U is the Coulomb interaction and W is the band width. This is supported by exact diagonalization and Monte Carlo calculations. Realistic parameters for the doped fullerenes lead to the conclusions that stoichiometric A3C60 (A=K, Rb) are near the Mott-Hubbard transition, in a correlated metallic state. 71.10.Fd, 71.30.+h,

The origin of the cooperative Jahn-Teller distortion and orbital order in LaMnO3 is central to the physics of the manganites. The question is complicated by the simultaneous presence of tetragonal and GdFeO3-type distortions and the strong Hund's rule coupling between e{g} and t{2g} electrons. To clarify the situation we calculate the transition temperature for the Kugel-Khomskii superexchange mechanism by using the local density approximation+dynamical mean-field method, and disentangle the effects of superexchange from those of lattice distortions. We find that superexchange alone would yield T{KK} approximately 650 K. The tetragonal and GdFeO3-type distortions, however, reduce T{KK} to approximately 550 K. Thus electron-phonon coupling is essential to explain the persistence of local Jahn-Teller distortions to greater than or approximately 1150 K and to reproduce the occupied orbital deduced from neutron scattering.

We analyze cellular dynamical mean-field theory ͑CDMFT͒ and the dynamical cluster approximation ͑DCA͒. We derive exact sum-rules for the hybridization functions and give examples for dynamical mean-field theory, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. Going from one to two dimensions we find that fitting the bath becomes in general significantly more difficult, requiring a large number of bath sites. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization.

The Mott insulating perovskite KCuF3 is considered the archetype of an orbitally ordered system. By using the local-density approximation+dynamical mean-field theory method, we investigate the mechanism for orbital ordering in this material. We show that the purely electronic Kugel-Khomskii super-exchange mechanism alone leads to a remarkably large transition temperature of T(KK) to approximately 350 K. However, orbital order is experimentally believed to persist to at least 800 K. Thus, Jahn-Teller distortions are essential for stabilizing orbital order at such high temperatures.