Neutral gap closing at large q for Haldane pseudopotentials

Determine whether the neutral spectral gap for the two-body Haldane pseudopotential Hamiltonians at filling fraction 1/q closes for larger values of q.

Background

Beyond the small-q regime addressed by Haldane’s conjecture, there is a contrasting expectation for large q within the Laughlin sequence. The authors highlight a conjecture that, as q increases, the neutral gap collapses. This reflects long-standing numerical and theoretical indications that higher-denominator Laughlin states may become gapless with respect to neutral excitations.

Clarifying the regime of gap closure versus uniform positivity as a function of q is essential for mapping the phase diagram of fractional quantum Hall states generated by Haldane pseudopotentials.