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

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.

12 pages, 8 figures; Submitted to EPJ Special Topics, Quantum Gases and Quantum Coherence

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• Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
• Simulation of two-boson bound states using arrays of driven-dissipative coupled linear optical resonators
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• Vortex bound states in dimerized $\pi$-flux optical lattices: characterization, state preparation and current measurement
• Topological bound states in a lattice of rings with nearest-neighbour interactions