Hard-Wall Confinement of a Fractional Quantum Hall Liquid

We make use of numerical exact diagonalization calculations to explore the physics of $\nu =1\mathrm{/}2$ 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.