Topological quantum slinky motion in the resonant extended Bose-Hubbard model

We study the one-dimensional Bose-Hubbard model under the resonant condition, where the nearest-neighbor and on-site interaction strengths are equal. In the strong interaction limit, $n$ bosons occupied in a single site can transfer to neighboring sites in a complete manner, which is referred to as quantum slinky motion. It can be shown that quantum slinky motions can be described by a set of effective noninteracting Hamiltonians. These Hamiltonians are sets of generalized Su-Schrieffer-Heeger chains with an $n$-site unit cell in an auxiliary space, referred to as trimerization, tetramerization, pentamerization, etc., possessing nontrivial 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.