# Three-body repulsive forces among identical bosons in one dimension

## TL;DR

This paper explores how three-body forces dominate the interactions among identical bosons in one dimension when two-body interactions are tuned to a special resonance, revealing that three-body repulsion prevents bound states and has implications for ultracold gases.

## Contribution

It demonstrates that the leading correction to the ground state energy in one-dimensional bosons with resonant interactions is due to emergent three-body forces, which are repulsive and prevent bound states.

## Key findings

- Three-body interactions dominate at resonance conditions.
- Emergent three-body forces are repulsive for realistic potentials.
- Results suggest possibilities for realizing pure three-body interactions experimentally.

## Abstract

I consider non-relativistic bosons interacting via pairwise potentials with infinite scattering length and supporting no two-body bound states. To lowest order in effective field theory, these conditions lead to non-interacting bosons, since the coupling constant of the Lieb-Liniger model vanishes identically in this limit. Since any realistic pairwise interaction is not a mere delta function, the non-interacting picture is an idealisation indicating that the effect of interactions is weaker than in the case of off-resonant potentials. I show that the leading order correction to the ground state energy for more than two bosons is accurately described by the lowest order three-body force in effective field theory that arises due to the off-shell structure of the two-body interaction. For natural two-body interactions with a short-distance repulsive core and an attractive tail, the emergent three-body interaction is repulsive and, therefore, three bosons do not form any bound states. This situation is analogous to the two-dimensional repulsive Bose gas, when treated using the lowest-order contact interaction, where the scattering amplitude exhibits an unphysical Landau pole. The avoidance of this state in the three-boson problem proceeds in a way that parallels the two-dimensional case. These results pave the way for the experimental realisation of one-dimensional Bose gases with pure three-body interactions using ultracold atomic gases.