Theory of correlations in strongly interacting fluids of two-dimensional dipolar bosons

Ground-state properties of a two-dimensional fluid of bosons with repulsive dipole-dipole interactions are studied by means of the Euler-Lagrange hypernetted-chain approximation. We present a self-consistent semi-analytical theory of the pair distribution function $g(r)$ and ground-state energy of this system. Our approach is based on the solution of a zero-energy scattering Schr\"{o}dinger equation for the "pair amplitude" $\sqrt{g(r)}$ with an effective potential from Jastrow-Feenberg correlations. We find excellent agreement with quantum Monte Carlo results over a wide range of coupling strength, nearly up to the critical coupling for the liquid-to-crystal quantum phase transition. We also calculate the one-body density matrix and related quantities, such as the momentum distribution function and the condensate fraction.