A hydrogenic chain in a non-orthogonal basis: Beyond the Hubbard model

 The Hubbard model was first proposed in a paper by J. Hubbard in 1963 to describe strong interactions between fermions on a lattice. We have extended these ideas by including the effects of overlaps between adjacent orbitals on a hydrogenic chain of atoms in a spirit similar to the derivation of the Pariser-Parr-Popple (PPP) model. As a consequence, the Schrödinger equation becomes a generalized eigenvalue problem. We orthogonalize the basis using a Löwdin transformation, resulting in a Hamiltonian with long-range hopping and interactions in real space that also breaks particle-hole symmetry. We study the implications on the metal-insulator transition in 1D and calculate spectral functions with the density matrix renormalization group (DMRG) method.