Many-body Aharonov-Bohm caging in a lattice of rings

We study a system of a few ultracold bosons loaded into states with orbital angular momentum l = 1 of a onedimensional staggered lattice of rings. Local eigenstates with winding numbers +l and -l form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle 0 of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective it flux through the plaquettes. We find nontrivial topological band structures and many-body Aharonov-Bohm caging in the N-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle 0 is introduced at an arbitrary lattice periodicity gamma. For gamma > 2, the pi flux becomes nonuniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.