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

• URL: http://arxiv.org/abs/2103.14711v3
• Date: Wed, 9 Jun 2021 10:50:21 GMT
• Title: Emergent four-body parameter in universal two-species bosonic systems
• Authors: Lorenzo Contessi, Johannes Kirscher, Manuel Pavon Valderrama
• Abstract summary: We study the existence of a scale unique to the $AABB$ tetramer. We understand the $AABB$ and $AAAB$/$ABBB$ tetramers as representatives of two different universal classes of $N$-body systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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