Orthogonalization of fermion k-body operators and representability
Published in Physical Review A, 2019
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.
Recommended citation: V. Bach and R. Rauch, “Orthogonalization of fermion k-body operators and representability,” Phys. Rev. A, vol. 99, no. 4, p. 042109, Apr. 2019. https://arxiv.org/abs/1807.05299