Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model

TL;DR

This paper evaluates the effectiveness of free auxiliary models, like the Kohn-Sham model, in representing interacting fermion systems, introducing the interaction distance to quantify their limitations and propose an optimal entanglement model.

Contribution

It introduces the interaction distance as a measure to assess free models' accuracy and proposes an optimal entanglement model for strongly correlated regimes.

Findings

Interaction distance quantifies Kohn-Sham model limitations.

Optimal free state reproduces entanglement properties.

Parent Hamiltonian enables accurate observable predictions.

Abstract

Density functional theory maps an interacting Hamiltonian onto the Kohn-Sham Hamiltonian, an explicitly free model with identical local fermion densities. Using the interaction distance, the minimum distance between the ground state of the interacting system and a generic free fermion state, we quantify the applicability and limitations of the exact Kohn-Sham model in capturing the various properties of the interacting system. As a byproduct, this distance determines the optimal free state that reproduces the entanglement properties of the interacting system as faithfully as possible. The parent Hamiltonian of the optimal free state identifies a system that can determine the expectation value of any observable with controlled accuracy. This optimal entanglement model opens up the possibility of extending the systematic applicability of auxiliary free models into the non-perturbative, strongly-correlated regimes.