标题： 分数量子霍尔流体中的量子几何涨落 显示英文标题

标题： Quantum geometric fluctuations in fractional quantum Hall fluids

摘要： 我们在这里提出了一种关于分数量子霍尔流体中一类中性激发的完整微观理论，这些激发与量子霍尔基态的几何涨落有关。 这些几何模式的许多物理性质可以被解析地推导出来。 这些包括这些几何模式的手征性、多重性和能量，以及它们与不可压缩和可压缩流体基态密度调制的关系，无论是否存在平移对称性（例如，气泡相和条纹相）。 特别关注最近实验测量的引力子模式这一特殊情况，我们阐明了这些几何模式的普遍特性以及依赖于微观哈密顿量细节的非普遍特性。 微观理论解释了有效场论和复合费米子理论中的一些现象学组成部分。 它预测了如何在不同能量尺度下的任何拓扑或可压缩相中通过实验测量具有两种手征性的几何或引力子模式。 特别是，我们展示了即使对于可压缩的分数量子霍尔相，也可以存在有能隙的几何模式，尽管基态的平移对称性对于这些模式在长波极限下与外部探测器（例如拉曼散射）耦合是重要的。 显示英文摘要

摘要： We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such geometric modes can be inferred analytically. These include the chirality, multiplicity and energy of these geometric modes, as well as the relationship to the density modulation of the ground states of both incompressible and compressible fluids, with or without translational symmetry (e.g. the bubble and stripe phases). With a particular focus on the recently experimentally measured graviton modes as the special case, we elucidate both the universal aspects of the geometric modes and the non-universal aspects dependent on the details of the microscopic Hamiltonians. The microscopic theory explains some of the phenomenological components in the effective field theory and composite fermion theory. It predicts how geometric or graviton modes of both chiralities can be measured in experiments for any topological or compressible phases at different energy scales. In particular we show gapped geometric modes can exist even for compressible FQH phases, though translational symmetry of the ground state is important for such modes to couple to external probes (e.g. Raman scattering) in the long wavelength limit.