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

Abstract

We study a system of a few ultracold bosons loaded into the states with orbital angular momentum $l=1$ of a one-dimensional 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 $\varphi$ 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 $\pi$-flux through the plaquettes. We find non-trivial 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 $\varphi$ is introduced at an arbitrary lattice periodicity $\Gamma$. For $\Gamma >2$, the $\pi$-flux becomes non-uniform, 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.

12 pages, 14 figures

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• Local Hilbert space fragmentation and weak thermalization in Bose-Hubbard diamond necklaces
• Effects of Peierls phases in open linear chains
• Flux-mediated effective Su-Schrieffer-Heeger model in an impurity decorated diamond chain
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• Impurity flat band states in the diamond chain
• Synthetic $\pi$-flux system in 2D superconducting qubit array with tunable coupling
• Topological bound states in a lattice of rings with nearest-neighbour interactions
• Controlled acoustic-driven vortex transport in coupled superfluid rings