  The influence of short-range Coulomb correlations on the Mott transition in
the single-band Hubbard model at half-filling is studied within cellular
dynamical mean field theory for square and triangular lattices.
Finite-temperature exact diagonalization is used to investigate correlations
within two-, three-, and four-site clusters. Transforming the non-local
self-energy from a site basis to a molecular orbital basis, we focus on the
inter-orbital charge transfer between these cluster molecular orbitals in the
vicinity of the Mott transition. In all cases studied, the charge transfer is
found to be small, indicating weak Coulomb induced orbital polarization despite
sizable level splitting between orbitals. These results demonstrate that all
cluster molecular orbitals take part in the Mott transition and that the
insulating gap opens simultaneously across the entire Fermi surface. Thus, at
half-filling we do not find orbital-selective Mott transitions, nor a
combination of band filling and Mott transition in different orbitals.
Nevertheless, the approach towards the transition differs greatly between
cluster orbitals, giving rise to a pronounced momentum variation along the
Fermi surface, in agreement with previous works. The near absence of Coulomb
induced orbital polarization in these clusters differs qualitatively from
single-site multi-orbital studies of several transition metal oxides, where the
Mott phase exhibits nearly complete orbital polarization as a result of a
correlation driven enhancement of the crystal field splitting. The strong
single-particle coupling among cluster orbitals in the single-band case is
identified as the source of this difference.
