Lifetime of quasi-bound states in the Bose-Hubbard case with finite interaction

Determine the lifetime of the three-particle quasi-bound states in the continuum that occur in the Bose-Hubbard case of the anyon-Hubbard model at zero statistical angle and finite on-site interaction.

Background

For finite repulsive interaction U=4J, the paper reports quasi-three-body bound states in the continuum even at statistical angle θ=0, corresponding to the Bose-Hubbard case. The numerical calculations identify these states but do not establish their thermodynamic-limit decay behavior.

The authors specifically state that the dependence of their lifetime on increasing system size remains to be investigated.

References

We find a plethora of bound state solutions both outside and inside the scattering state continua for various statistical angles $\theta$, where, interestingly, we also find (quasi-) three-body bound states in the continuum (qBIC) for the Bose-Hubbard case $\theta=0$, whose lifetime for larger system sizes has to be investigated in future work.

— Few-body bound states in the anyon-Hubbard model  (2609.09125 - Tesfaye et al., 8 Sep 2026) in Appendix, subsection Three-particle spectrum for finite on-site interaction