Semiclassical Analysis of Quantum Dimer Models*

We use the slave boson approach to develop the semiclassical description of the Rokshar Kivelson square lattice quantum dimer model, which allows a 1/S expansion. The action reproduces a generalized height representation. We extend these results to the dimer model on the cubic lattice, where we obtain emergent quantum electrodynamics description. The estimated speed of light: c = S/2*Sqrt[(J−V)J]. We confirm aspects of the height mapping such as the correlation between the sign of the terms in the height action and the sign of the potential term in the RK Hamiltonian. In dimensions D = 2, 3 the QED emerges at wave vectors (π,π) and (π,π,π) respectively. Our estimate of the RK parameter is 1/16 which is within a 20 to 30 percent of the exact value of 1/4π. We extend our analysis to the hexagonal and diamond lattices, and we find that the speed of light for the diamond lattice is given by c^2 = S^4*[(J − V )J]/64.