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Journal of Physics A Mathematical and General

Traces of the reduced density operators revisited: closed-form formulae

Josep Planelles, Jacek Karwowski

Published May 7, 1997• 2 citations
Publisher

Abstract

Closed-form expressions for traces of the qth-order reduced density operators, q-RDOs, and symmetry-adapted q-RDOs calculated in an N-electron and spin-adapted subspace of a K-orbital Fock space are derived. The asymptotic form of the expression for traces of the q-RDOs, corresponding to and limits, is discussed in detail. Several identities fulfilled by some quantities related to the traces are derived.

DOI
10.1088/0305-4470/30/9/027

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Closed-form expressions for traces of the qth-order reduced density operators, q-RDOs, and symmetry-adapted q-RDOs calculated in an N-electron and spin-adapted subspace of a K-orbital Fock space are derived. The asymptotic form of the expression for traces of the q-RDOs, corresponding to and limits, is discussed in detail. Several identities fulfilled by some quantities related to the traces are derived.
The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ2 and Ŝz operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.
The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ2 and Ŝz operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.
In our previous studies with the evaluation of traces of p-order replacement operators calculated in finite-dimensional, antisymmetric, and spin-adapted N-electron spaces (p\ensuremath{\le}N), we described a technique for the calculation of those expressions based on the reduction of the opertor order [A. Torre, L. Lain, and J. Millan, Phys. Rev. A 47, 923 (1993)]. Now, we report a general formula which, condensing all the reduction steps, leads to the direct evaluation of those traces. Some examples for illuminating the usefulness of that formula are reported.