EQUIVALENCE OF THE DIMER RESONATING-VALENCE-BOND PROBLEM TO THE QUANTUM ROUGHENING PROBLEM

A geometric mapping of dimers on a square lattice onto surfaces of a 3D crystal is constructed. The mapping transforms the dimer-RVB (resonating valence bond) problem to the quantum roughening problem: Low-energy excitations correspond to the crystal surface fluctuations; holes are represented by screw dislocations. A phase diagram is discussed and the existence of a quantum-liquid state with gapless excitations is demonstrated using the results obtained previously for the roughening problem. © 1990 The American Physical Society.