  The parton theory constructs candidate fractional quantum Hall states by
decomposing the physical particles into unphysical partons, placing the partons
in integer quantum Hall states, and then gluing the partons back into the
physical particles. Field theoretical formulations execute the gluing process
through the device of emergent gauge fields. Here we study numerically the
process of going from the integer quantum Hall effect of two species of
fermionic partons to the fractional quantum Hall effect of bosons by
introducing an attractive interaction between the fermions of different species
and continuously increasing its strength to glue them into bosons. To properly
capture the physics in the bulk, we implement this process in a lattice version
of the spherical geometry, which allows us to keep the full Hilbert space. Even
though the two end-point states are topologically distinct, we find that, for
the small system sizes accessible to our study, the energy gap remains open,
indicating a crossover between these two states.
