COLUMNAR DIMER AND PLAQUETTE RESONATING-VALENCE-BOND ORDERS IN THE QUANTUM DIMER MODEL

We study the nature of the ground state of the quantum dimer model pro posed by Rokhsar and Kivelson by diagonalizing the Hamiltonian of the model on square lattices of size LxL, where L less than or equal to 8, with periodic boundary conditions. Finite-size scaling studies of the columnar order parameter and the low lying excitation spectrum show n o evidence of a dimer liquid state in any finite region of the zero te mperature phase diagram. In addition, we find evidence of a transition from the columnar dimer state to an intermediate state at a negative value of V/J. This state is consistent with the plaquette resonating-v alence-bond state. The energy gap of this state vanishes as a power la w of L. It exhibits columnar dimer order, but has disorder within the dimer columns. This state persists up to V/J<1, and the system changes to a dimer liquid state only at V/J=1.