  We examine whether the Mott transition of a half-filled, two-orbital Hubbard
model with unequal bandwidths occurs simultaneously for both bands or whether
it is a two-stage process in which the orbital with narrower bandwith localizes
first (giving rise to an intermediate `orbital-selective' Mott phase). This
question is addressed using both dynamical mean-field theory, and a
representation of fermion operators in terms of slave quantum spins, followed
by a mean-field approximation (similar in spirit to a Gutzwiller
approximation). In the latter approach, the Mott transition is found to be
orbital-selective for all values of the Coulomb exchange (Hund) coupling J when
the bandwidth ratio is small, and only beyond a critical value of J when the
bandwidth ratio is larger. Dynamical mean-field theory partially confirms these
findings, but the intermediate phase at J=0 is found to differ from a
conventional Mott insulator, with spectral weight extending down to arbitrary
low energy. Finally, the orbital-selective Mott phase is found, at
zero-temperature, to be unstable with respect to an inter-orbital
hybridization, and replaced by a state with a large effective mass (and a low
quasiparticle coherence scale) for the narrower band.
