In this review, the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ([Formula: see text]-wave) Cooper pairing and are characterized by non-Abelian statistics of their quasiparticles. Here we focus on conditions for their realization and competition among them at half-integer filling factors. Using the Dirac composite fermion description, in the presence of a mass term, we study the influence of Landau level mixing in selecting a particular Pfaffian state. While Pfaffian and anti-Pfaffian are selected when Landau level mixing is not strong, and can be taken into account perturbatively, the particle–hole (PH) Pfaffian state requires non-perturbative inclusion of at least two Landau levels. Our findings, for small Landau level mixing, are in accordance with numerical investigations in the literature, and call for a non-perturbative approach in the search for PH Pfaffian correlations. We demonstrated that a method based on the Chern–Simons field-theoretical approach can be used to generate characteristic interaction pseudo-potentials for Pfaffian paired states.

中文翻译：

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半整数分数量子霍尔效应的 Pfaffian 配对状态

在这篇综述中，在分数量子霍尔效应的背景下，Pfaffian 配对态的物理学使用场论方法进行了讨论。Pfaffian 状态是拓扑（[公式：见文本]-波）Cooper 配对的主要例子，并以其准粒子的非阿贝尔统计为特征。在这里，我们关注它们的实现条件和它们之间在半整数填充因子上的竞争。使用狄拉克复合费米子描述，在存在质量项的情况下，我们研究了朗道能级混合对选择特定普法夫态的影响。虽然当朗道能级混合不强时选择 Pfaffian 和反 Pfaffian，并且可以考虑微扰，但粒子-空穴 (PH) Pfaffian 状态需要非微扰包含至少两个朗道能级。我们的发现，对于小朗道水平混合，与文献中的数值研究一致，并要求在搜索 PH Pfaffian 相关性时采用非微扰方法。我们证明了一种基于 Chern-Simons 场理论方法的方法可用于生成 Pfaffian 配对状态的特征相互作用赝势。