环形晶格中的多体阿哈罗诺夫-玻姆囚禁
Many-body Aharonov-Bohm caging in a lattice of rings
AI总结：
本文研究超冷玻色子在交错环形晶格中轨道角动量态上的多体阿哈罗诺夫-玻姆囚禁，通过调节中心角ϕ产生有效π通量，揭示非平凡拓扑能带结构并推广到任意晶格周期Γ的情形。
摘要：
我们研究了一个系统，其中少量超冷玻色子被装载到一维交错环形晶格中轨道角动量 $l=1$ 的态上。具有绕数 $+l$ 和 $-l$ 的局域本征态形成一个具有一个实维度与一个合成维度的 Creutz 梯子。相邻环中绕数相反的态通过复隧穿耦合，这种耦合可以通过改变晶格的中心角 $ϕ$ 来调节。我们利用微扰理论分析了单粒子情形以及强相互作用区域下的少玻色子束缚态子空间，展示了如何通过设计系统几何结构来在 plaquette 中产生有效的 $π$ 通量。我们发现，即使在单粒子谱具有色散的情况下，$N$ 粒子子空间中仍然存在非平凡的拓扑能带结构和多体阿哈罗诺夫-玻姆囚禁。此外，我们研究了在任意晶格周期 $Γ$ 下引入角度 $ϕ$ 的一类模型。对于 $Γ>2$，$π$ 通量变得非均匀，随着谱中平带数目的增加，阿哈罗诺夫-玻姆囚禁的空间范围也随之扩大。所有解析结果均通过精确对角化进行了基准验证。
英文摘要：
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.
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