  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 (FQH) phases. The conformal
invariance of these subspaces are derived explicitly from microscopic many-body
states. The resultant 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 $\nu=1/3$ and $\nu=2/5$, 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 $\nu=2/5$, 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.
