Orthogonalization of fermion k-body operators and representability

TL;DR

This paper constructs explicit orthonormal bases for fermion Fock space operators, facilitating the understanding of the k-body reduced density matrix and addressing the long-standing representability problem in quantum chemistry.

Contribution

It provides an explicit orthonormal basis for fermion Fock space operators that restricts to k-body operators for all k, aiding the study of the representability problem.

Findings

Explicit orthonormal basis for fermion Fock space operators constructed.

Basis restricts to k-body operators for all k.

Facilitates understanding of the reduced k-particle density matrix.

Abstract

The reduced k-particle density matrix of a density matrix on finite-dimensional, fermion Fock space can be defined as the image under the orthogonal projection in the Hilbert-Schmidt geometry onto the space of k-body observables. A proper understanding of this projection is therefore intimately related to the representability problem, a long-standing open problem in computational quantum chemistry. Given an orthonormal basis in the finite-dimensional one-particle Hilbert space, we explicitly construct an orthonormal basis of the space of Fock space operators which restricts to an orthonormal basis of the space of k-body operators for all k.