# Site-occupation--Green's function embedding theory: A density-functional approach to dynamical impurity solvers

## TL;DR

This paper introduces SOGET, a Green's function-based extension of density-functional theory for impurity problems, which is formally exact and reduces computational costs by avoiding many-body wavefunctions.

## Contribution

The paper develops SOGET, a Green's function embedding approach that is formally exact and simplifies calculations by eliminating the need for many-body wavefunctions.

## Key findings

- Successfully applied to the one-dimensional Hubbard model
- Uses a local density-functional approximation combining Bethe Ansatz and Anderson model
- Reduces computational cost compared to previous methods

## Abstract

A reformulation of site-occupation embedding theory (SOET) in terms of Green's functions is presented. Referred to as site-occupation--Green's function embedding theory (SOGET), this novel extension of density-functional theory for model Hamiltonians shares many features with dynamical mean-field theory (DMFT) but is formally exact (in any dimension). In SOGET, the impurity-interacting correlation potential becomes a density-functional self-energy which is frequency-dependent and in principle non-local. A simple local density-functional approximation (LDA) combining the Bethe Ansatz (BA) LDA with the self-energy of the two-level Anderson model is constructed and successfully applied to the one-dimensional Hubbard model. Unlike in previous implementations of SOET, no many-body wavefunction is needed, thus reducing drastically the computational cost of the method.