Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom

TL;DR

This paper explores a natural extension of the Hartree-Fock method based on fermionic occupation number constraints, demonstrating its application to the lithium atom and deriving universal bounds on correlation energy.

Contribution

It introduces a novel variational ansatz based on generalized Pauli constraints and applies it to the lithium atom, revealing simplified structures and universal energy bounds.

Findings

The ansatz simplifies the fermionic state structure at the boundary of allowed occupation numbers.

Universal geometrical bounds on correlation energy are derived from the mathematical structure.

Application to lithium atom shows promising results for the new approach.

Abstract

Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed region the corresponding $N$-fermion quantum state has a significantly simpler structure. We recall the recently proposed natural extension of the Hartree-Fock ansatz based on this structural simplification. This variational ansatz is tested for the lithium atom. Intriguingly, the underlying mathematical structure yields universal geometrical bounds on the correlation energy reconstructed by this ansatz.