Topological quantum slinky motion in resonant extended Bose-Hubbard model

We study the one-dimensional Bose-Hubbard model under the resonant condition, where a series of quantum slinky oscillations occur in a two-site system for boson numbers $n\in \lbrack 2,\infty )$. In the strong interaction limit, it can be shown that the quantum slinky motions become the dominant channels for boson propagation, which are described by a set of effective non-interacting Hamiltonians. They are sets of generalized Su-Schrieffer-Heeger chains with an $n$-site unit cell, referred to as trimerization, tetramerization, and pentamerization, etc., possessing non-trivial Zak phases. The corresponding edge states are demonstrated by the $n$-boson bound states at the ends of the chains. We also investigate the dynamic detection of edge boson clusters through an analysis of quench dynamics. Numerical results indicate that stable edge oscillations clearly manifest the interaction-induced topological features within the extended Bose-Hubbard model.