| Abstract: | A spin-free symmetry-adapted valence bond (VB ) state, named bonded tableau (BT ), is deduced from the classical bonded function and labeled by an at most two-column Weyl tableau. The complete set, which is composed of the BT basis or canonical bonded tableau (CBT ), can be constructed from an overcomplete set of BT states. CI CBT and VB CBT are two kinds of complete sets that are constructed in this paper. They can be used, respectively, in the CI and VB theory. It is shown that there is a one-to-one correspondence between the labeling scheme for CI CBT and the Gelfand–Tsetlin (GT ) basis. This relationship enables an efficient generation and compact representation of the BT basis if one desires to use the known global representation scheme for the GT basis. Effective algorithms for the matrix element evaluation of unitary group generators and products of generators between BT states are presented. In the formulation, the action of a generator on a BT state yields another BT state times a coefficient, so that the matrix elements of an arbitrary multiple product of generators are reduced to a calculation of the overlaps between BT states. The evaluation of the overlaps leads to a simple factorization into cycle contributions, whose values are given explicitly and only depend on the length parameters of the cycles. It is hoped that the presented formalism can facilitate the procedures for handling of the many-electron correlation problem. |
