  We derive a "Wannier-Hubbard" model consisting of an array of overlapping
atomic orbitals interacting via a local Coulomb interaction. Transforming to an
orthogonal Wannier basis set, the resulting Hamiltonian displays long range
hopping and interactions, with new terms such as correlated hopping and
ferromagnetic direct exchange, among others. We numerically study the
one-dimensional version of the model at half-filling using the density matrix
renormalization group (DMRG) method, unveiling a rich phase diagram as a
function of the interaction $U$ and the overlap $s$ with metallic, and
ferromagnetic phases, separated by a ferrimagnetic region. Our results indicate
a path toward understanding new emergent phases under pressure and beyond
standard model Hamiltonians.
