Exact results for a quantum Hall state with broken rotational symmetry
Exact results for a quantum Hall state with broken rotational symmetry
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DOI：
10.1016/j.jpcs.2019.02.021
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发表时间：
2019-07-01
影响因子：
4
通讯作者：
Ciftja, Orion
中科院分区：
文献类型：
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作者：
Ciftja, Orion
强关联二维电子系统中最强的分数量子霍尔态出现在最低朗道能级的三分之一填充因子处。这种状态的特征在于电子的各向同性量子液相，并通过Laughlin波函数很好地描述。通过不具有旋转对称性的多体试探波函数，也考虑了电子在不同填充因子下各向异性液相的可能性。采用不同的方法和计算方法进行了几项研究。具有破缺旋转对称性的波函数的固有多体性质使得解析计算非常麻烦。在这项工作中，我们成功地精确计算了每个粒子的总能量和所有其他相关的量，这些量对应于由旋转对称性破缺的波函数描述的三分之一填充因子的两个电子的量子系统。所获得的结果作为基准，以衡量用于研究这种性质的强相关电子系统的性能的各种数值方法和模拟技术的准确性。
The most robust fractional quantum Hall state in a strongly correlated two-dimensional system of electrons occurs at one-third filling factor of the lowest Landau level. This state is characterized as an isotropic quantum liquid phase of electrons and is well-described by Laughlin's wave function. The possibility of anisotropic liquid phases of electrons at various filling factors has also been considered via many-body trial wave functions that do not possess rotational symmetry. Several studies employing different approaches and computational methods have been carried out. The inherent many-body nature of a wave function with broken rotational symmetry makes it very cumbersome for analytic calculations. In this work we succeeded to calculate exactly the total energy per particle and all other relevant quantities that correspond to a quantum system of two electrons at one-third filling factor described by a wave function with broken rotational symmetry. The results obtained serve as benchmarks to gauge the accuracy of various numerical methods and simulation techniques used to study the properties of strongly correlated electronic systems of this nature.