Multiple impurities and combined local density approximations in Site-Occupation Embedding Theory

TL;DR

This paper advances Site-Occupation Embedding Theory by generalizing it to multiple impurity sites and developing new density-functional approximations, tested with DMRG, showing improved accuracy across various correlation regimes.

Contribution

The work introduces a multi-impurity extension of SOET and a novel combined 2L-BALDA density-functional approximation, enhancing the theory's accuracy and applicability.

Findings

The combined 2L-BALDA DFA outperforms previous functionals in all regimes.

Self-consistent DMRG calculations validate the new approximations.

Detailed error analysis highlights the strengths of the combined 2L-BALDA approach.

Abstract

Site-occupation embedding theory (SOET) is an in-principle-exact multi-determinantal extension of density-functional theory for model Hamiltonians. Various extensions of recent developments in SOET [Senjean et al., Phys. Rev. B 97, 235105 (2018)] are explored in this work. An important step forward is the generalization of the theory to multiple impurity sites. We also propose a new single-impurity density-functional approximation (DFA) where the density-functional impurity correlation energy of the two-level (2L) Hubbard system is combined with the Bethe ansatz local density approximation (BALDA) to the full correlation energy of the (infinite) Hubbard model. In order to test the new DFAs, the impurity-interacting wavefunction has been computed self-consistently with the density matrix renormalization group method (DMRG). Double occupation and per-site energy expressions have been derived and implemented in the one-dimensional case. A detailed analysis of the results is presented, with a particular focus on the errors induced either by the energy functionals solely or by the self-consistently converged densities. Among all the DFAs (including those previously proposed), the combined 2L-BALDA is the one that performs the best in all correlation and density regimes. Finally, extensions in new directions, like a partition-DFT-type reformulation of SOET, a projection-based SOET approach, or the combination of SOET with Green functions, are briefly discussed as a perspective.