Columnar dimer and plaquette resonating valence bond states of the quantum dimer model

We study the nature of the ground state of the quantum dimer model proposed by Rokhsar and Kivelson by diagonalizing the Hamiltonian of the model on square lattices of size $L\times L$, where $L\leq 8$, with periodic boundary conditions. Finite-size scaling studies of the columnar order parameter and the low lying excitation spectrum show no evidence of a dimer liquid state in any finite region of the zero temperature 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 identified to be the plaquette resonating valence bond (RVB) state. The energy gap of this state vanishes as a power law of $L$. It exhibits columnar dimer order, but has disorder {\it within} the dimer columns. This state persists up to $V/J<1$, and the system changes to a dimer liquid state only at $V/J=1$.