Ground-state properties of Bose liquids with long-range interactions in d spatial dimensions

We consider a low-density system of Bose particles in general dimensionality interacting through a potential having a short-range part and a long-range tail that falls off like 1/rs, focusing mainly on the special case s=2. We use a renormalization-group approach for the computation of the ground-state properties, which we argue is asymptotically exact in the dilute limit. The strength of the long-range part determines fixed-point values for the amplitude of the short-range part; several phases can occur, depending on the relative strengths of the short-range part and the fixed-point amplitudes. For the case in which the physics is determined by the flow away from the unstable fixed point (or when there are no fixed points at all), there results a collapsed state. When the flow is towards the stable fixed point, the outcome depends on whether the fixed-point value is negative or positive: In the former case we predict a kind of bound state, which is characterized by nontrivial correlations, even though the particles are not pairwise bound; in the latter case, a density expansion for the ground-state properties is given. The leading term of this expansion gives an exact result (a generalization of the one-dimensional result previously given by Sutherland) whenever the renormalization flow ends at the stable fixed point (including in particular the case that the flow starts at the fixed point). For the case that the renormalization flow stops before reaching the fixed point, the expansion parameter is proportional to the density raised to a nonuniversal power. The case s>2 can be reduced to the treatment of purely short-range interactions, whereas the repulsive case of s<2 cannot be handled without additionally introducing a background of opposite charge. The case of attraction for s<2 always leads to a collapse.