Liu Zhao, Möller Gunnar, Bergholtz Emil J
Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
Functional Materials Group, School of Physical Sciences, University of Kent, Canterbury CT2 7NZ, United Kingdom.
Phys Rev Lett. 2017 Sep 8;119(10):106801. doi: 10.1103/PhysRevLett.119.106801. Epub 2017 Sep 7.
We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.
我们研究了外在的类虫洞扭曲缺陷，这些缺陷在多组分分数量子霍尔系统的晶格版本中有效地增加了空间的亏格。尽管这些缺陷会使原始能带结构发生畸变，导致带隙中的局域态，但我们发现，通过调节局部单粒子势，可以设计出一个代表更高亏格系统的新的最低平带。值得注意的是，一旦开启这个新能带中的局部多体相互作用，我们就能识别出各种阿贝尔和非阿贝尔分数量子霍尔态，其基态简并度会随着缺陷数量的增加而增加，也就是随着空间的亏格增加。拓扑简并度对缺陷的这种敏感性提供了一个“概念验证”，证明了拓扑场论所预测的作为与空间变化拓扑相关的奇异非阿贝尔缺陷的类子，确实存在于现实的微观模型中。具体而言，我们的结果表明，可以通过将冷原子系统中人工规范场的物理与现有的用于产生扭曲缺陷的全息光束整形方法相结合，在实验室中产生类子。
