有限距离上的准费米零模的重叠
Overlap of parafermionic zero modes at a finite distance
摘要：
仿费米子束缚态是马约拉纳束缚态的推广，在近似分数量子霍尔边缘态中，它被预言为零能量本征态。类似于MBS，PBS之间的有限距离可以分裂基态简并性。然而，parafermionic模式有一个更丰富的交换统计比MBS，所以几个相互作用项是允许的潜在的$\mathbb{Z}_{2n}$对称性，使有效的哈密顿量管理一对PBS在一个有限的距离非平凡。在这里，我们使用的分析技术（半经典瞬子近似）和数值技术（量子蒙特卡罗模拟）的组合，以确定有效的耦合哈密顿量。为了这个目的，我们超越了稀释的一瞬子气体近似，并显示如何有限尺寸的影响，可以引起更高阶的parafermion相互作用。我们发现分析结果和蒙特卡罗模拟之间非常吻合。我们估计，这些有限尺寸的修正应该是可观察到的，在最近提出的实验中观察强相关系统中的光子带隙。
英文摘要：
Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying $\mathbb{Z}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.
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