Abstract
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 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 emergent phases under pressure and beyond standard model Hamiltonians.
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