title: 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.
authors.affiliation: Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400005, India.
authors.forename: Kedar
authors.initials: K
authors.lastname: Damle
authors.forename: Deepak
authors.initials: D
authors.lastname: Dhar
authors.forename: Kabir
authors.initials: K
authors.lastname: Ramola