Exploring universal and non-universal regimes of trimers from three-body interactions in one-dimensional lattices

TL;DR

This paper studies the formation and properties of three-particle bound states (trimers) in a one-dimensional lattice model with two- and three-body interactions, revealing regimes of universal and non-universal behavior relevant to Rydberg atoms and polar molecules.

Contribution

It identifies conditions for stable large and small trimers in a 1D lattice with specific interactions, and describes their behavior across different interaction regimes, including continuum and scattering descriptions.

Findings

Large trimers are stabilized for attractive U and positive V.

Small trimers are bound for attractive U and V.

Bound-state behavior transitions from scattering states to compact dimers with increasing |U|.

Abstract

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbour two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\leq-2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\rightarrow \infty$, while both attractive $U\leq0$ and $V\leq0$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\rightarrow -\infty$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V>>t$, $U<-2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.