Resonating valence-bond physics on the honeycomb lattice

Abstract

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|^η_w(2), where Q=(2π/3,−2π/3) is the wave vector corresponding to “columnar” valence-bond solid order on the honeycomb lattice, and η_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 D^d(⃗r) of this dimer model has power-law behavior D^d(⃗r)∼cos(Q⋅⃗r)/|⃗r|^η_d(2) with η_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.