Static correlated functionals for reduced density matrix functional theory

TL;DR

This paper introduces a new class of correlation functionals for reduced density matrix functional theory, leveraging fermionic exchange symmetry to explicitly express the wave-function and correlation energy, with successful tests on a three-electron Hubbard model.

Contribution

It develops novel functionals based on saturation of generalized Pauli constraints, enabling explicit wave-function expressions for odd-electron systems.

Findings

Excellent performance in weak and strong correlation regimes

Accurate correlation energy calculations for a three-electron Hubbard model

Demonstrates the potential of exchange symmetry-based functionals

Abstract

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and natural orbitals. This leads to an expression for the two-particle density matrix and therefore for the correlation energy functional. This functional was then tested for a three-electron Hubbard model where it showed excellent performance both in the weak and strong correlation regimes.