  We investigate fractional quantum Hall states for model interactions
restricted to a repulsive hard-core. When the hard-core excludes relative
angular momentum $m=1$ between spinless electrons the ground state at Landau
level filling factor $\nu=1/3$ is known to be exactly given by the Laughlin
wavefunction. When we exclude relative angular momentum three only, W\`ojs,
Quinn and Yi have suggested the appearance of a liquid state with non-Laughlin
correlations. We study this special hard-core interaction at filling factor 1/3
on the sphere, torus and cylinder geometry. An analysis of the charged and
neutral gaps on the sphere geometry points to a gapless state. On the torus
geometry the projected static structure factor has a two-peak feature pointing
to one-dimensional density ordering. To clarify the nature of the ground state
we perform extended DMRG studies on the cylinder geometry for up to 30
particles. The pair correlation function allows us to conclude that the ground
state is a two-particle bubble phase.
