Resonating valence bond wave functions and classical interacting dimer models

Abstract

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 V₂(g) favoring two parallel dimers on elementary plaquettes. For SU(2) spins, using our calculated value of V₂(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/|⃗r|^α with α≈1.22. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give α≈1.20.