Groundhyphen;state features for Heisenberg models

摘要

Isotropic Heisenberg models with nearesthyphen;neighbor interactions between spins located at the vertices of a bipartite (or alternant) graph are considered. Six theorems helping characterize the ground state are given. Building upon the theorems of Lieb and Mattis concerning the rsquo;rsquo;nodelessnessrsquo;rsquo; of the wave functions and their spin symmetry, we establish related results concerning certain expectation values and rsquo;rsquo;point grouprsquo;rsquo; symmetries. Applications especially concerning valencehyphen;bond descriptions of the pgr;hyphen;electron systems of organic molecules, are briefly indicated.