Inverse mean field theories

In this work we discuss the extraction of mean field single particle Hamiltonians from a many body wave function of a fermionic system. While we primarily discuss lattice models we also look at neon in an augccpvdz basis set as an example. Our approach allows us to discuss the result of a many particle wave function in terms of a non-interacting description. In contrast to density functional theory approaches on the lattice this approach allows the extraction of appropriate kinetic terms. In result the extracted mean field theories are closer to the physics of the problem under investigation. Therefore, the extracted mean field Hamiltonians may provide an improved starting point for perturbative approaches. In addition, the technique can be used to decide whether a density matrix renormalization group calculation for interacting fermions has converged to the true ground state.