谐振势阱中相互作用二维凝聚玻色子-晶格系统的拓扑边态显示
Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap
摘要：
在这封信中，它表明，相互作用可以促进出现的拓扑边缘状态的量子简并玻色子系统中存在的谐波势。在合成规范场下，用自旋一玻色子填充的六角晶格的具体模型证明了这种效应。在费米子或非相互作用系统中，谐波陷阱的存在会使边缘态的观测变得模糊。对于我们的弱相互作用玻色子系统，我们可以清楚地看到一个拓扑能带结构，带隙被边缘态穿过。我们还发现，当存在谐波陷阱时，穿过带隙的边缘态数目增加，并且边缘模在穿过第一布里渊区时经历了能量移动，这与系统的拓扑性质有关.我们找到了一个边缘态能量的解析表达式，并与数值计算结果进行了比较，结果显示出良好的一致性。
英文摘要：
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas--Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
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