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arXiv 1903.04876cond-mat.str-elcond-mat.quant-gas
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双柱磁通阶梯中的前拓扑分数激发

Pretopological fractional excitations in the two-leg flux ladder

Marcello Calvanese Strinati, Sharmistha Sahoo, Kirill Shtengel, Eran Sela

摘要:

拓扑序是分数量子霍尔态的标志,主要是根据更高亏格流形(例如环面)上的基态简并来定义的。我们研究分析和数值光滑的交叉之间的拓扑政权和陶-无薄环面准一维极限。利用线构造方法,分析了表征拓扑序崩溃的电荷密度波(CDW),并将其相移与威尔逊圈算符联系起来。当CDW振幅超过线间耦合控制的横向相关长度时,CDW振幅随环周长呈指数下降。通过基于矩阵乘积态(MPS)理论的数值模拟,我们探索了两足流梯中的准一维极限,并给出了探测硬核玻色子类$ν=1/2$ Laughlin态分数电荷激发的一个简单方法.我们讨论了在冷原子实验中实现这种结构的可能性。我们还讨论了我们的发现对产生非阿贝尔零模式的可能性的影响。从严格的no-go定理可知,在一维费米子系统中不可能存在对奇异零模(如parafermion)的拓扑保护,并且相关的简并性也不可能是稳健的。我们的1D-2D交叉理论允许计算简并度的分裂,简并度随着线的数量呈指数消失,类似于CDW振幅。

英文摘要:

Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between this topological regime and the Tao-Thouless thin torus quasi-1D limit. Using the wire-construction approach, we analyze an emergent charge density wave (CDW) signifying the break-down of topological order, and relate its phase shifts to Wilson loop operators. The CDW amplitude decreases exponentially with the torus circumference once it exceeds the transverse correlation length controllable by the inter-wire coupling. By means of numerical simulations based on the matrix product states (MPS) formalism, we explore the extreme quasi-1D limit in a two-leg flux ladder and present a simple recipe for probing fractional charge excitations in the $ν=1/2$ Laughlin-like state of hard-core bosons. We discuss the possibility of realizing this construction in cold-atom experiments. We also address the implications of our findings to the possibility of producing non-Abelian zero modes. As known from rigorous no-go theorems, topological protection for exotic zero modes such as parafermions cannot exist in 1D fermionic systems and the associated degeneracy cannot be robust. Our theory of the 1D-2D crossover allows to calculate the splitting of the degeneracy, which vanishes exponentially with the number of wires, similarly to the CDW amplitude.

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