# Bubble phase at $\nu=1/3$ for a spinless hollow-core interaction

## TL;DR

This paper explores a special hard-core interaction in fractional quantum Hall systems at filling factor 1/3, revealing a bubble phase ground state through numerical analysis.

## Contribution

It demonstrates that excluding relative angular momentum three leads to a bubble phase at ν=1/3, contrasting with the Laughlin state for other interactions.

## Key findings

- Ground state is gapless on the sphere geometry.
- Static structure factor indicates one-dimensional density order on the torus.
- Numerical simulations confirm a two-particle bubble phase on the cylinder.

## Abstract

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.