Many-body Aharonov-Bohm caging in a lattice of rings
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arXiv
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| Format: | Preprint |
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2022
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| author | Nicolau, Eloi Marques, Anselmo M. Dias, Ricardo G. Mompart, Jordi Ahufinger, Verònica |
| author_facet | Nicolau, Eloi Marques, Anselmo M. Dias, Ricardo G. Mompart, Jordi Ahufinger, Verònica |
| contents | 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 $ϕ$ 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 $π$-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 $ϕ$ is introduced at an arbitrary lattice periodicity $Γ$. For $Γ>2$, the $π$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_09183 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Many-body Aharonov-Bohm caging in a lattice of rings Nicolau, Eloi Marques, Anselmo M. Dias, Ricardo G. Mompart, Jordi Ahufinger, Verònica Quantum Gases 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 $ϕ$ 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 $π$-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 $ϕ$ is introduced at an arbitrary lattice periodicity $Γ$. For $Γ>2$, the $π$-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. |
| title | Many-body Aharonov-Bohm caging in a lattice of rings |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2209.09183 |