Two-body bound and edge states in the extended SSH Bose-Hubbard model

TL;DR

This paper investigates two-body bound states in an extended SSH Bose-Hubbard model, revealing novel edge-bound states caused by the interplay of lattice geometry and interactions, with implications for topological quantum systems.

Contribution

It introduces the existence of edge-bound states in the extended SSH Bose-Hubbard model due to combined on-site and nearest-neighbor interactions, supported by exact diagonalization and perturbation theory.

Findings

Two classes of bound states identified

Edge-bound states persist in strong interaction regimes

Energy crossings analyzed with exact methods

Abstract

We study the bosonic two-body problem in a Su-Schrieffer-Heeger dimerized chain with on-site and nearest-neighbor interactions. We find two classes of bound states. The first, similar to the one induced by on-site interactions, has its center of mass on the strong link, whereas the second, existing only thanks to nearest-neighbors interactions, is centered on the weak link. We identify energy crossings between these states and analyse them using exact diagonalization and perturbation theory. In the presence of open boundary conditions, novel strongly-localized edge-bound states appear in the spectrum as a consequence of the interplay between lattice geometry, on-site and nearest-neighbor interactions. Contrary to the case of purely on-site interactions, such EBS persist even in the strongly interacting regime.