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

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.