Pseudo-potentials modeling fractional quantum Hall systems are quantum many-body Hamiltonians with an at most fractionally filled ground state. In addition to translation invariance, they are characterized by two symmetries related to the conservation of charge and dipole moment. We show that generally, for such systems, the minimum energy of charged excitations is bounded below by that of neutral excitations. This property, which had been repeatedly observed in numerical simulations, has a surprisingly simple proof based on the interplay of the above symmetries and the fractional maximal filling. 

(Based on joint work with Bruno Nachtergaele, Marius Lemm, and Amanda Young, arxiv:2410.11645).