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 $\nu =\frac{1}{3}$ is known to be exactly given by the Laughlin wave function. When we exclude relative angular momentum 3 only, Wójs, 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 $\frac{1}{3}$ 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 density matrix renormalization group 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.

• Received 22 March 2017
• Revised 19 June 2020
• Accepted 17 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.245107