Many-anyon quasi-bound states in the continuum at large particle number

Determine whether quasi-bound states in the continuum of the anyon-Hubbard model persist for sufficiently large particle number and become asymptotically stabilized as the particle number increases.

Background

The paper observes that three- and four-body quasi-bound states in the continuum can be very long-lived in finite systems, although three-body states are not true bound states in the continuum in the thermodynamic limit. The authors propose that, for increasing particle number, localization at a zero-dimensional corner of the relative-coordinate space might increase the lifetimes of such states.

Whether this geometric mechanism produces persistent or asymptotically stable many-anyon clusters is not resolved. The question is posed as a possible alternative to energetic stabilization by attractive interactions.

References

This latter scenario also opens another question, namely whether the many-anyon model might feature weak ergodicity breaking or prethermalization, possibly related to the physics of correlated hopping models or kinetically constrained models with many-body (Aharonov-Bohm-like) Fock space cages, where the latter are already present in the simplest two-particle configuration space lattice.

— Few-body bound states in the anyon-Hubbard model  (2609.09125 - Tesfaye et al., 8 Sep 2026) in Section Summary and Outlook