Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals

TL;DR

This paper introduces a local potential functional embedding theory (LPFET) based on density-functional theory for lattice systems, improving upon previous methods in certain regimes but still facing challenges in describing the Mott-Hubbard transition.

Contribution

The paper derives a density-functional version of Ht-DMFET, formulates LPFET, and demonstrates its performance and limitations in modeling electron correlation and gap opening in lattice systems.

Findings

LPFET outperforms Ht-DMFET in low-density, strongly correlated regimes.

Both methods fail to describe the Mott-Hubbard transition.

A single impurity can describe gap opening if the correlation potential exhibits a derivative discontinuity.

Abstract

The recently proposed Householder transformed density-matrix functional embedding theory (Ht-DMFET) [Sekaran et al., Phys. Rev. B 104, 035121 (2021)], which is equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, is revisited from the perspective of density-functional theory (DFT). An in-principle-exact density-functional version of Ht-DMFET is derived for the one-dimensional Hubbard lattice with a single embedded impurity. On the basis of well-identified density-functional approximations, a local potential functional embedding theory (LPFET) is formulated and implemented. Even though LPFET performs better than Ht-DMFET in the low-density regime, in particular when electron correlation is strong, both methods are unable to describe the density-driven Mott-Hubbard transition, as expected. These results combined with our formally exact density-functional embedding theory reveal that a single statically embedded impurity can in principle describe the gap opening, provided that the complementary correlation potential (that describes the interaction of the embedding cluster with its environment, which is simply neglected in both Ht-DMFET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work.