Higher-order effective interactions for bosons near a two-body zero crossing

We develop the perturbation theory for bosons interacting via a weak two-body potential V, attractive and repulsive parts of which cancel each other. We find that the leading nonpairwise contribution to the energy emerges in the third order in V and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of V. We apply our theory to a few particular two-body interaction potentials and calculate the leading two-body and three-body interaction corrections for tilted dipoles in quasi-low-dimensional geometries. We show that our approach is consistent with the many-body Bogoliubov treatment.

Automated summary

This study develops perturbation theory for bosons interacting through a weak two-body potential V with attractive and repulsive components that cancel each other out. The leading nonpairwise energy contribution arises in the third order of V, presenting an effective three-body interaction. This interaction is generally found to exhibit an opposite sign to the long-range tail of V, and the theory is applied to specific two-body potentials for calculating interaction corrections. The approach is shown to be consistent with the many-body Bogoliubov treatment.