Ground-state properties of the O(2) lattice model in two dimensions:A correlated-basis-function approach

We study the ground-state properties of the O(2) model for a system of spin-1 rotors on a simple square lattice. We assume that the rotors interact via nearest-neighbor forces, the coupling characterized by a strength parameter λ. This many-boson model can be physically realized, for example, through a two-dimensional configuration of Josephson junction arrays or superfluid ⁴He in confined geometries. The formal and numerical analysis of the model concentrates on a study of the strong correlations induced by the interactions. The theoretical investigation is performed within a semianalytic ab initio approach employing the theory of correlated basis functions, on the variational level. In the past the formalism has been successfully applied for quantitative analyses of spatial correlations in quantum fluids. In the present work it is formally adapted for treating the O(2) model. We express the ground-state energy by an appropriate functional in terms of the reduced on-site density profile and of the site-site distribution function. Employing the familiar minimum principle for the ground-state energy we construct two associated Euler-Lagrange equations which determine the optimal correlated ground-state of Hartree-Jastrow type. We present solutions of these equations and numerical results on various ground-state properties as functions of the coupling strength λ. We discuss in detail the behavior of the density profile and of the site-site distribution function. We also report data on the order parameter for the symmetry-broken ordered phase and on the critical strength λ_c for the transition to the disordered phase.