Neutral gap as the lowest excitation energy in fractional quantum Hall systems

Ascertain whether, in fractional quantum Hall systems at maximal fractional filling, the neutral spectral gap in the fixed particle-number sector equals the lowest excitation energy across the full system over all particle-number sectors.

Background

In fractional quantum Hall systems, the energy difference between the ground state and the first excited state within the same particle-number sector at maximal fractional filling is known as the neutral gap. It is widely believed that this neutral excitation sets the overall lowest excitation energy of the system, typically associated with magneto-roton modes.

The authors note that this identification is a conjecture; their main result, proving that the charge gap dominates the neutral gap under broad structural assumptions, supports this picture but does not, by itself, settle the identification across all possible excitations and sectors in all models referred to as FQHS.