A sparse framework for the derivation and implementation of fermion algebra

Abstract

Algorithms useful in the construction of electron correlation models are collected alongside new developments for cases of high rank and sparsity. In the first part of this paper a Brandow diagram manipulation program is presented. The complementary second section describes a general-rank sparse contraction algorithm which exploits the permutational symmetries of many-fermion quantities. Several recently published local correlation models (perfect quadruples and perfect hextuples) were built using these codes. This paper should facilitate reproduction and extension of high-rank electron correlation models that combine truncation by level of substitution with truncation by locality, such as the number of entangled electron pairs.

Keywords:

• symbolic computation
• coupled-cluster
• complete active space
• perfect pairing

Acknowledgements

This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract DE-AC0376SF00098, and by a grant from the SciDac Program.