Properties of resonating-valence-bond spin liquids and critical dimer models

We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare with the classical dimer model (CDM). The latter system also corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at its critical point. We find that, although spin-spin correlations decay exponentially in the RVB, four-spin valence-bond-solid correlations are critical, qualitatively like the well-known dimer-dimer correlations of the CDM, but decaying more slowly (as 1/r(alpha) with alpha approximate to 1.20, compared with alpha = 2 for the CDM). We also compute the distribution of monomer (defect) pair separations, which decay by a larger exponent in the RVB than in the CDM. We further study both models in their different winding-number sectors and evaluate the relative weights of different sectors. Like the CDM, all the observed RVB behaviors can be understood in the framework of a mapping to a height model characterized by a gradient-squared stiffness constant K. Four independent measurements consistently show a value K-RVB approximate to 1.6K(CDM), with the same kinds of numerical evaluations of K-CDM giving results in agreement with the rigorously known value K-CDM = pi/16. The background of a nonzero winding-number gradient W/L introduces spatial anisotropies and an increase in the effective K, both of which can be understood as a consequence of anharmonic terms in the height-model free energy, which are of relevance to the recently proposed scenario of Cantor deconfinement in extended quantum dimer models. In addition to the standard case of short bonds only, we also studied ensembles in which fourth-neighbor (bipartite) bonds are allowed at a density controlled by a tunable fugacity, resulting (as expected) in a smooth reduction of K.