一般分数量子Hall系统中的三体相互作用及伽利略不变性破缺的影响
Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking
摘要：
利用Schriffan-Wolff变换，推导了分数量子霍尔（FractionalQuantumHall，HHH）系统中朗道能级（Landau Level，LL）混合的三体相互作用的完整解析表达式。形式主义可以适用于任何LL，非常一般的系统没有旋转或伽利略不变性。我们说明了如何三体赝势（PPs）可以很容易地从各种不同的系统的解析表达式计算，并表明，对于现实的系统，软化裸库仑相互作用（例如，有限厚度或屏蔽）可以显着抑制三体相互作用。更有趣的是，对于没有伽利略不变性的实验系统（这在实际材料中很常见），有强有力的证据表明，更高阶的能带色散可以将摩尔-里德态从反普夫朗相驱动到普夫朗相。我们的分析点的重要性，现实的能带结构的细节，非阿贝尔拓扑相位，我们推导出的解析表达式也可以是非常有用的高保真度的数值计算。
英文摘要：
We derive full analytic expressions of three-body interactions from Landau level (LL) mixing in fractional quantum Hall (FQH) systems with Schrieffer-Wolff transformation. The formalism can be applied to any LL, and to very general systems without rotational or Galilean invariance. We illustrate how three-body pseudopotentials (PPs) can be readily computed from the analytical expressions for a wide variety of different systems, and show that for realistic systems, softening the bare Coulomb interactions (e.g. finite thickness or screening) can significantly suppress three-body interactions. More interestingly, for experimental systems without Galilean invariance (which is common for real materials), there is strong evidence that higher orders in band dispersion can drive the Moore-Read state from anti-Pfaffian to Pfaffian phase. Our analysis points to the importance of the realistic band structure details to the non-Abelian topological phases, and the analytical expressions we derived can also be very useful for high fidelity numerical computations.
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