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

TL;DR

This paper develops a perturbation theory for bosons with near-zero two-body interactions, revealing that the leading nonpairwise energy contribution appears at third order as an effective three-body interaction, with sign depending on the potential's tail.

Contribution

It introduces a perturbative framework for analyzing higher-order interactions in bosonic systems near a two-body zero crossing, including explicit results for specific potentials.

Findings

Effective three-body interactions emerge at third order in perturbation theory.

The sign of the three-body term is often anticorrelated with the tail of the potential.

Explicit calculations are provided for particular potentials and tilted dipoles.

Abstract

We develop the perturbation theory for bosons interacting via a two-body potential $V$ of vanishing mean value. 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 $V$. Explicit results are obtained for a few particular two-body interaction potentials and we perform a detailed perturbative analysis of tilted dipoles in quasi-low-dimensional geometries.