Introducing screening in one-body density matrix functionals: impact on the Extended Koopmans' Theorem's charged excitations of model systems

TL;DR

This paper investigates how reduced density matrix functionals influence the accuracy of charged excitation energies obtained via the Extended Koopmans' Theorem, highlighting a new approximation that improves band gap predictions in strongly correlated systems.

Contribution

The study introduces a new approximation combining RPA screening with the Power functional to improve EKT band gap estimates in correlated materials.

Findings

Exact density matrices lead to overestimated band gaps.

Approximate density matrices benefit from error cancellation.

The new approximation reduces EKT band gap overestimation.

Abstract

In this work we get insight into the impact of reduced density matrix functionals on the quality of removal/addition energies obtained using the Extended Koopmans' Theorem (EKT). Within reduced density matrix functional theory (RDMFT) the EKT approach reduces to a matrix diagonalization, whose ingredients are the one- and two-body reduced density matrices. A striking feature of the EKT within RDMFT is that it opens a band gap, although too large, in strongly correlated materials, which are a challenge for state-of-the-art methods such as GW . Using the one-dimensional Hubbard model and the homogeneous electron gas as test cases, we find that: i) with exact or very accurate density matrices the EKT systematically overestimates the band gap in the Hubbard model and the bandwidth in the homogeneous electron gas; ii) with approximate density matrices, instead, the EKT can benefit from error cancellation. In particular we test a new approximation which combines RPA screening with the Power functional (PF) approximation to the two-body reduced density matrix introduced by Sharma et al. [Phys. Rev. B 78, 201103(R) (2008)]. An important feature of this approximation is that it reduces the EKT band gap in the studied models; it can hence be a promising approximation for correcting the EKT band-gap overestimation in strongly correlated materials.