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

• Published in: arXiv.org
• Main Authors: Contessi, Lorenzo, Kirscher, Johannes, Manuel Pavon Valderrama
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 09.06.2021
• Subjects: Binding energy; Bosons; Clusters; Correlation; Parameters; Physics - Atomic and Molecular Clusters; Physics - Nuclear Theory; Physics - Quantum Gases; Physics - Quantum Physics; Trimers
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2103.14711

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.