Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations

TL;DR

This paper develops and tests a site-occupation embedding theory (SOET) framework using Bethe ansatz approximations, providing a new way to combine wavefunction methods with density-functional theory for the Hubbard model.

Contribution

It introduces exact expressions for key energies in SOET and constructs Bethe ansatz-based approximations, advancing the modeling of correlated electron systems.

Findings

Promising results in specific correlation and density regimes.

Effective approximations for the bath contribution to correlation energy.

Potential for improved embedding functionals and potentials.

Abstract

Site-occupation embedding theory (SOET) is an alternative formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a non-interacting) one. It provides a rigorous framework for combining wavefunction (or Green function) based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wavefunction has been performed with the density matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.