Generalized Pauli constraints in reduced density matrix functional theory

TL;DR

This paper investigates the impact of enforcing pure-state N-representability conditions, known as generalized Pauli constraints, on reduced density matrix functional theory calculations for three-electron systems, comparing results with and without these constraints.

Contribution

It assesses how enforcing pure-state conditions affects the accuracy of 1-RDM functional calculations, a novel exploration in the context of generalized Pauli constraints.

Findings

Pure-state conditions can influence correlation energy calculations.

Enforcing pure-state constraints alters optimal occupation numbers.

Comparison shows differences between ensemble-only and combined constraints.

Abstract

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman's ensemble $N$-representability conditions. Recently, the topic of pure-state $N$-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble $N$-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.