Emergent four-body parameter in universal two-species bosonic systems

TL;DR

This paper investigates the universal properties of two-species bosonic systems, revealing a new four-body parameter for the AABB tetramer that breaks previous three- and four-body scale correlations.

Contribution

It demonstrates the emergence of a unique four-body scale in two-species bosonic systems, challenging the assumption of universal three-body correlations.

Findings

The AABB tetramer's binding energy is not constrained by three-body scales.

A new four-body parameter is predicted for the AABB tetramer.

Different classes of N-body systems exhibit distinct scaling properties.

Abstract

The description of unitary few-boson systems is conceptually simple: only one parameter -- the three-body binding energy -- is required to predict the binding energies of clusters with an arbitrary number of bosons. Whether this correlation between the three- and many-boson systems still holds for two species of bosons for which only the inter-species interaction is resonant depends on how many particles of each species are in the system. For few-body clusters with species $A$ and $B$ and a resonant $AB$ interaction, it is known that the emergent $AAB$ and $ABB$ three-body scales are correlated to the ground-state binding energies of the $AAAB$ and $ABBB$ systems, respectively. We find that this link between three and four bodies is broken for the $AABB$ tetramer whose binding energy is neither constrained by the $AAB$ nor by the $ABB$ trimer. From this de-correlation, we predict the existence of a scale unique to the $AABB$ tetramer. In our explanation of this phenomenon, we understand the $AABB$ and $AAAB$/$ABBB$ tetramers as representatives of two different universal classes of $N$-body systems with distinct renormalization-group and discrete-scaling properties.