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Journal of Physics A Mathematical and General

Traces of powers of the Hamiltonian operator in finite-dimensional antisymmetric model spaces

Fernando Rajadell, Josep Planelles, Jacek Karwowski

Published Aug 7, 1993• 11 citations
Publisher

Abstract

A general method of evaluation of traces of arbitrary powers of Hermitian operators containing one- and two-body interactions and defined in a finite-dimensional model space is presented. The model space is taken as the antisymmetric and spin-adapted part of an N-fold Cartesian product of a one-electron space. The method is based on the symmetric group approach to the theory of many-electron systems.

DOI
10.1088/0305-4470/26/15/036

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Physical Review A•Sep 1, 1995•11 citations
A general method of evaluation of traces of arbitrary powers of Hermitian operators containing one- and two-body interactions and defined in a finite-dimensional model space is presented. The model space is taken as the antisymmetric and spin-adapted part of an N-fold Cartesian product of a one-electron space. The method is based on the symmetric group approach to the theory of many-electron systems.
An N-electron Hamiltonian projected onto a K-orbital, antisymmetric and spin-adapted model space (in quantum chemistry known as the full configuration interaction space) may be expressed as a linear combination of products of generators of the unitary group . Consequently, spectral density distribution moments and other quantities which characterize global properties of the Hamiltonian spectra in are defined by the averages over the model space of products of the generators. This paper presents a set of new recurrent formulae for the averages and describes a simple graphical method of their evaluation.
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.