Landau Levels in Lattices with Long Range Hopping
Landau Levels in Lattices with Long Range Hopping
复制标题
具有长程跳跃的格子中的朗道能级
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Oktel
中科院分区：
文献类型：
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作者：
Hakan Atakicsi;M. Oktel
在存在周期性势的朗道能级 (LL) 的情况下，朗道能级 (LL) 会变宽，从而为使用光学晶格中的冷原子精确模拟分数量子霍尔效应形成障碍。最近，研究表明，如果引入特定形式的长程跳跃，最低朗道能级 (LLL) 的简并性可以在紧密结合晶格中恢复 (E. Kapit 和 E. J. Mueller, Phys. Rev. Lett. 105, 215303 (2010))。在本文中，我们研究了与晶格中此类量子霍尔父哈密顿量相关的三个问题。首先，我们证明存在无限多个长程跳跃模型，其中通过连续 LLL 中波函数的晶格离散化形成大规模简并流形。然后我们给出了构建此类模型的通用方法，该方法不仅适用于 LLL，而且适用于更高的 LL。我们使用这种方法给出恢复 LLL 的跳频的解析表达式，以及下一个 LL 的积分表达式。我们还考虑了离散LL波函数所跨越的空间是否与连续波函数所跨越的空间一样大，并找到了满足该条件的磁场约束。最后，使用这些约束和第一个陈数，我们确定了
In the presence of a periodic potential Landau levels (LLs) are broadened, forming a barrier for accurate simulation of fractional quantum Hall eect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight binding lattice, if a particular form of long range hopping is introduced (E. Kapit and E. J. Mueller, Phys. Rev. Lett. 105, 215303 (2010)). In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are innitely many long range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wavefunctions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restore the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wavefunctions is as large as the space spanned by continuum wavefunctions and nd the constraints on magnetic eld for this condition to be satised. Finally, using these constraints and rst Chern numbers, we identify the bands of