Gapless Edge Gravitons and Quasiparticles in Fractional Quantum Hall Systems with Non-Local Confinement

One of the central tenets of the theory of the fractional quantum Hall effect is that the bulk quantized Hall response requires the existence of a gapless chiral edge mode. The field theoretical arguments for this rely on locality. While locality is typically met in standard experimental settings, it need not always apply. Motivated by experimental capabilities of photonic platforms, we study confining potentials that are step-like in angular momentum, and thus non-local in position. We show that this non-local potential does not host conventional chiral edge modes. These are replaced by gapless spin-2 edge states, which we show are connected to the collective 'graviton' excitations that are gapped in the bulk. Furthermore, we show that FQH states host gapless (charged) quasiparticles on their edges, even in the absence of conventional edge modes. The edge state energies vanish as a power-law in system size, with an exponent that characterises the bulk topological order.