On Csanyi's and Arias' Functional for Ground States Energy of Multi-Particle Fermion Systems: Asymptotics

TL;DR

This paper establishes bounds for Csanyi's and Arias' energy functional in multi-particle fermion systems, deriving an asymptotic expansion of the ground state energy that aligns with quantum energy up to third order.

Contribution

It introduces bounds for Csanyi's and Arias' functionals and derives an asymptotic expansion matching quantum energy to third order.

Findings

Csanyi's and Arias' functional is bounded by Muller and Hartree-Fock functionals.

An asymptotic expansion of the ground state energy is derived.

The expansion agrees with quantum energy up to third order.

Abstract

We show that Csanyi's and Arias' energy functional of the reduced one-particle density matrix is bounded from below by the M\"uller functional and bounded from above by the Hartree-Fock functional. We use this fact to derive an asymptotic expansion of the ground state energy of this functional which agrees with the quantum energy to third order.