  Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and
to construct low-energy effective Hubbard-like models. The downfolding
procedure first involves a change of basis to a set of atom-centered Wannier
functions constructed from the natural orbitals of the exact DMRG one-particle
density matrix. The Wannier function model is then reduced to a fewer-parameter
Hubbard-like model, whose parameters are determined by minimizing the
expectation value of the Wannier Hamiltonian in the ground state of the Hubbard
Hamiltonian. This indirect variational procedure not only yields compact and
simple models for the hydrogen chain, but also allows us to explore the
importance of constraints in the effective Hamiltonian, such as the restricting
the range of the single-particle hopping and two-particle interactions, and to
assess the reliability of more conventional downfolding. The entanglement
entropy for a model's ground state, cut in the middle, is an important property
determining the ability of DMRG and tensor networks to simulate the model, and
we study its variation with the range of the interactions. Counterintuitively,
we find that shorter ranged interactions often have larger entanglement.
