Resonating Valence Bond Wave Functions and Classical Interacting Dimer Models

We relate properties of nearest-neighbor resonating valence-bond (NNRVB) wave functions for SU(g) spin systems on two-dimensional bipartite lattices to those of fully packed interacting classical dimer models on the same lattice. The interaction energy can be expressed as a sum of n-body potentials V-n, which are recursively determined from the NNRVB wave function on finite subgraphs of the original lattice. The magnitude of the n-body interaction V-n (n > 1) is of order O(g(-(n-1))) for small g(-1). The leading term is a two-body nearest-neighbor interaction V-2(g) favoring two parallel dimers on elementary plaquettes. For SU(2) spins, using our calculated value of V-2(g = 2), we find that the long-distance behavior of the bond-energy correlation function is dominated by an oscillatory term that decays as 1/vertical bar(r) over right arrow vertical bar(alpha) with alpha approximate to 1.22. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give alpha approximate to 1.20.