Low-energy effective models for 2D hydrogen square lattices derived from first principles

Effective model Hamiltonians use a small set of interactions to represent the physics of strongly correlated systems. To accurately represent real materials, effective models can be downfolded from first-principles calculations; however, using current methods, it can be difficult to assess systematic errors of the resulting models. The density matrix downfolding (DMD) procedure addresses this challenge by allowing the use of standard statistical analysis tools to quantify the errors of effective models fit to first-principles data [1].

We have applied DMD to a computationally simple strongly correlated material, a 2D finite square lattice of hydrogen. The energy spectra of the resulting tight-binding and Hubbard effective models were compared against first-principles data. Our results show that for 2D square hydrogen, the addition of the on-site electron interaction term U greatly improves the fit of the effective model.

[1] H. Zheng et. al., Front. Phys. 6, 43 (2018).