Resonating Valence-Bond Physics On The Honeycomb Lattice

We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric S = 1/ 2 antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form D(= r) = cos(Q = = r)/| = r|.w(2), where Q = (2p/ 3,-2p/ 3) is the wave vector corresponding to " columnar" valence-bond solid order on the honeycomb lattice, and.w (2) = 1.49(3). We use a recently introduced large-g expansion approach to relate bond-energy correlators of the SU(g) wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength V (g) = -ln(1 + 1/ g2). Putting g = 2, we find numerically that the dimer correlation function Dd (= r) of this dimer model has power-law behavior Dd (= r) = cos(Q = = r)/| = r|.d (2) with.d (2) = 1.520(15), in rather good agreement with the wave function results. We also study the same quantities for g = 3,4,10 and find that the bond-energy correlations in the SU(g) wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.