We motivate a close look on the usefulness of the Gaffnian and Haffnian quasihole manifold (null spaces of the respective model Hamiltonians) for well-known gapped fractional quantum Hall phases. The conformal invariance of these subspaces is derived explicitly from microscopic many-body states. The resultant conformal field theory (CFT) description leads to an intriguing emergent primary field with $h=2,c=0$, and we argue the quasihole manifolds are quantum mechanically well defined and well behaved. Focusing on the incompressible phases at $\nu =\frac{1}{3}$ and $\frac{2}{5}$, we show the low-lying excitations of the Laughlin phase are quantum fluids of Gaffnian and Haffnian quasiholes, and give a microscopic argument showing that the Haffnian model Hamiltonian is gapless against Laughlin quasielectrons. We discuss the thermal Hall conductance and shot-noise measurements at $\nu =\frac{2}{5}$, and argue that the experimental observations can be understood from the dynamics within the Gaffnian quasihole manifold. A number of detailed predictions on these experimental measurements are proposed, and we discuss their relationships to the conventional CFT arguments and the composite fermion descriptions.

中文翻译：

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Gaffnian和Haffnian：非unit形共形场理论与不可压缩分数量子霍尔效应的物理相关性

我们将密切关注加夫年和哈夫年准孔流形（各个模型哈密顿量的零空间）对众所周知的带隙分数量子霍尔相的有用性。这些子空间的共形不变性是明确地从微观多体状态得出的。由此产生的共形场理论（CFT）描述导致了一个引人入胜的新兴主场$H=\mathrm{2个}，C=0$，并且我们认为准孔流形在量子力学上具有良好的定义和良好的行为。专注于$\nu =\frac{\mathrm{1个}}{3}$ 和 $\frac{\mathrm{2个}}{5}$，我们证明了Laughlin相的低激发是Gaffnian和Haffnian准空穴的量子流体，并给出了微观论证，表明Haffnian模型哈密顿量对Laughlin准电子是无间隙的。我们在下面讨论霍尔热传导率和散粒噪声的测量$\nu =\frac{\mathrm{2个}}{5}$，并认为可以从Gaffnian拟孔流形内的动力学来理解实验观察结果。提出了许多关于这些实验测量的详细预测，并且我们讨论了它们与常规CFT参数和复合费米子描述的关系。