  It is commonly assumed in the studies of the fractional quantum Hall effect
that the physics of a fractional quantum Hall state, in particular the
character of its excitations, is invariant under a continuous deformation of
the Hamiltonian during which the gap does not close. We show in this article
that, at least for finite systems, as the interaction is changed from a model
three body interaction to Coulomb, the ground state at filling factor $\nu=2/5$
evolves continuously from the so-called Gaffnian wave function to the composite
fermion wave function, but the quasiholes alter their character in a
nonperturbative manner. This is attributed to the fact that the Coulomb
interaction opens a gap in the Gaffnian quasihole sector, pushing many of the
states to very high energies. Interestingly, the states below the gap are found
to have a one-to-one correspondence with the composite fermion theory,
suggesting that the Gaffnian model contains composite fermions, and that the
Gaffnian quasiholes are unstable to the formation of composite fermions when a
two-body interaction term is switched on. General implications of this study
are discussed.
