Interwoven limit cycles in the spectra of mass imbalanced many-boson system

The independence between few-body scales beyond the van der Waals universality is demonstrated for the extreme mass-imbalanced case of a specific many-boson system. This finding generalizes the scaling properties of universal tetramers to a broader class of heterogeneous few-boson systems. We assume two heavy atoms interacting with $(N-2)-$lighter ones at the unitary limit, using a particular case where no interactions are active between identical particles, by investigating the interwoven spectra of this many-body system for an arbitrary number of light bosons. A large mass-ratio between the particles allows us to treat this $N-$body system analytically, by solving an effective inverse-squared long-range interaction which is stablished for the two heavy bosons. For a cluster with $N-2$ light bosons ($N\ge 4$), we discuss the implications of the corresponding long-range potentials associated with different subsystem thresholds, implying in independent interwoven limit cycles for the correlation between the energies of excited $N-$body system. Our study with extreme mass-imbalanced few-boson bound states provides a fundamental understanding of the scaling behavior of their interwoven spectra. The novel insights enlarge the well-known Efimov physics paradigm and show the existence of different limit cycles, which could be probed by new experiments.