Precise spectral asymptotics, exponential localization, and spectral gap estimates for the three-boson lattice Schr"odinger operator
This research analyzed a three-boson Schrödinger operator on a two-dimensional lattice ($\mathbb{Z}_2$) with contact interactions at two specific quasimomenta, $K=0$ and $K=\pi$. The study found distinct spectral behaviors: exactly two bound states and exponential localization at $K=0$, contrasting with only one bound state at $K=\pi$. This reveals a spectral phase transition dependent on the mass ratio.