Constrained Hilbert Spaces and Many-body Scars in a Landau Level

We study a "pair-hopping" model that arises within a Landau level in the thin-torus limit of the quantum Hall effect. At filling \nu = 1/3, we show that the model maps on to the "PXP model", a constrained model for the Rydberg atom chain known to exhibit quantum many-body scars (ETH-violating states in the middle of the spectrum). Further, for general fillings factors \nu = p/(2p+1), we show the mapping onto spin-chains with constrained Hilbert spaces that share several features with the PXP model, including the presence of many-body scars and slow thermalization of particular product states. Finally, we investigate the stability of scars in the presence of electrostatic and long-range hopping terms that are always present in the quantum Hall setup.