Constructing Hubbard Models for the Hydrogen Chain using Sliced Basis DMRG

TL;DR

This paper uses sliced-basis DMRG to derive simplified Hubbard models for hydrogen chains, analyzing how interaction range constraints affect model accuracy and entanglement properties.

Contribution

It introduces a variational downfolding method to construct effective Hubbard models from DMRG data, exploring the impact of interaction constraints and entanglement.

Findings

Shorter ranged interactions can have larger entanglement.

The variational procedure produces compact, reliable Hubbard models.

Constraints on interaction range influence model accuracy and entanglement.

Abstract

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.