Orthogonalization of fermion k-body operators and representability

Volker Bach and Robert Rauch
Phys. Rev. A 99, 042109 – Published 9 April 2019

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.

  • Figure
  • Received 10 October 2018

DOI:https://doi.org/10.1103/PhysRevA.99.042109

©2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Volker Bach* and Robert Rauch

  • Technische Universität Braunschweig, Universitätsplatz 2, 38106 Braunschweig, Germany

  • *v.bach@tu-braunschweig.de
  • r.rauch@tu-braunschweig.de

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Issue

Vol. 99, Iss. 4 — April 2019

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