Transformation to bond variables
Department of Theoretical Physics,
Indian Association for the Cultivation of Science
2 Department of Applied Mathematics, University of Calcutta 92 Acharya Prafulla Chandra Road, Calcutta-700009, India
Accepted: 28 February 2002
Valence bonds are the basic entities in many chemical compounds. In a linear array of atoms translational invariance tells us the bonds have to be superposed. These superposed bond variables are shown to satisfy a closed algebra. We use a natural parameter in the algebra to truncate it. This allows us to transform the Hamiltonian of electrons into the Hamiltonian of bonds. Comparing the solutions, we establish the validity of the truncation procedure. The quantum bonds are obtained by superposing valence bonds with arbitrary phases. We demonstrate that these quantum valence bonds satisfy an extended algebra that admits truncation. The electron Hamiltonian is recast in terms of the quantum bonds and solved.
PACS: 31.15.Rh – Valence bond calculations / 36.20.-r – Macromolecules and polymer molecules / 02.20.Tw – Infinite-dimensional Lie groups
© EDP Sciences, 2002