Dimer State in Quantum Spin Systems

Abstract

The dimer state for the spin-1/2 quantum Heisenberg antiferromagnet is studied using the theory of resonating valence bond. The present theory is systematic and much more simple than the other theories. We obtain two important theorems. By use of them we can get the dimer eigen state in the linear chain, ladder, square and simple cubic lattices by the unified way. If the relations between exchange integrals are satisfied, the obtained dimer eigen state is the ground state.