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Bimetric Theory of Fractional Quantum Hall States

机译：分数量子厅态的双透明理论

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摘要

We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP) mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à?la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k 6 order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH) transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.
机译：我们提出了一个分数量子霍尔（FQH）的分数低能量有效理论，其描述了拓扑特性和螺纹集体激励，称为GIRVIN-MACDONALD-PLATZMAN（GMP）模式。该理论由拓扑Chern-Simons动作组成，耦合到对称秩-2张量，以及用于旋转-2模式的堵波动态的动作àΔLaΔLabimetric重力。该理论在弯曲的环境空间中配制，并且是空间的协调性，这使我们能够限制有效作用的形式和现象学系数的值。使用双金属理论，我们在势头扩展中计算投影静态结构因子直至k 6阶。为了提供对该理论的进一步支持，我们得出了GMP代数的长波极限，GMP模式的色散关系以及FQH状态的霍尔粘度。该理论的粒子孔（pH）变换采用非常简单的形式，使得FQH状态与其pH共轭物的二元性。我们还对分数Chern Insulators的可能申请发表评论，其中产生了密切相关的结构。结果表明，熟悉的FQH可观察可在双季度形式中获取奇怪的几何解释。

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