Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6

TL;DR

This paper provides an analytic proof of the Borland-Dennis conditions for 3-representability of a one-particle density matrix with rank 6, linking N-representability to Weyl's problem and Schubert calculus.

Contribution

It offers a new analytic proof of necessary conditions for 3-representability, connecting quantum chemistry with geometric methods like Schubert calculus.

Findings

Proves Borland-Dennis conditions are necessary for 3-representability.

Links N-representability problem to Weyl's problem and Schubert calculus.

Provides insights into general conditions for N-representability.

Abstract

An analytic proof is given of the necessity of the Borland-Dennis conditions for 3-representability of a one particle density matrix with rank 6. This may shed some light on Klyachko's recent use of Schubert calculus to find general conditions for N-representability.