Matrix product state representation of quasielectron wave functions
Matrix product state representation of quasielectron wave functions
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准电子波函数的矩阵积态表示
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. H. Hansson
中科院分区：
文献类型：
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作者：
Jonas A. Kjall;E. Ardonne;Vatsal Dwivedi;M. Hermanns;T. H. Hansson
矩阵乘积态技术提供了一种非常有效的方法来数值计算某些类型的量子霍尔波函数，这些函数可以写成二维共形场论中的相关器。重要的例子是Laughlin和Moore-Read基态及其准空穴激发。在本文中，我们将矩阵乘积态技术扩展到计算准电子波函数，这是一项更复杂的任务，因为相应的共形场论算符不是局域的。我们用我们的方法得到了具有多个准电子和准空穴的态的密度分布，并高精度地计算了激发的(相互)统计相位。我们研究的波函数受制于一个已知的困难：一个准电子的位置取决于其他准粒子的存在，即使它们的间距与磁长相比很大。用复合费米子图像构造的准电子波函数在拓扑上与我们研究的准电子是等价的，也有同样的问题。这一缺陷是严重的，因为它给出了通过编织遥远的准粒子获得的统计相的错误结果。我们详细地分析了这个问题，并指出它源于拓扑电荷的不完全屏蔽，这使得等离子体的类比无效。我们证明，当准粒子之间的间隔很大时，这是可以补救的，这使得我们能够获得正确的统计相位。最后，我们提出，允许局域准电子算符的Laughlin态的修正对于任意组态的激发都应该具有良好的拓扑性质。
Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.