Searching for new conditions for fermion N-representability

TL;DR

This paper introduces new necessary conditions for fermion N-representability of 2-density operators, demonstrating their strength for N=3 and suggesting an intrinsic link between eigenvalues and eigenfunctions.

Contribution

It proposes new elements of the dual cone of N-representable 2-density operators, enhancing the understanding of N-representability conditions, especially for N=3.

Findings

New conditions are stronger than known B- and C-conditions for 3-representability.

Evidence of an intrinsic relation between eigenvalues and eigenfunctions in spectral decomposition.

Results advance the theoretical framework of fermion N-representability.

Abstract

New elements of the dual cone of the set of fermion N-representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N-representability is obtained for N=3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction. keywords: fermion N-representability problem, conditions for N-representability