# Hard-Wall Confinement of a Fractional Quantum Hall Liquid

## TL;DR

This paper uses numerical exact diagonalization to study how hard-wall confinement affects the properties of a bosonic fractional quantum Hall droplet at filling factor 1/2, revealing unique spectral and density features.

## Contribution

It provides the first detailed analysis of FQH droplets under realistic hard-wall confinement, highlighting differences from harmonic traps and uncovering novel density depletions.

## Key findings

- Weak confinement lifts degeneracies and organizes excited states via Jack polynomials.
- Strong confinement causes spatial deformation and central density depletion.
- Hard-wall confinement leads to distinct spectral and density behaviors compared to other traps.

## Abstract

We make use of numerical exact diagonalization calculations to explore the physics of $\nu = 1/2$ bosonic fractional quantum Hall (FQH) droplets in the presence of experimentally realistic cylindrically symmetric hard-wall potentials. This kind of confinement is found to produce very different many-body spectra compared to a harmonic trap or the so-called extremely steep limit. For a relatively weak confinement, the degeneracies are lifted and the low-lying excited states organize themselves in energy branches that can be explained in terms of their Jack polynomial representation. For a strong confinement, a strong spatial deformation of the droplet is found, with an unexpected depletion of its central density.