Uniform Laughlin gap and stability under bounded scalar disorder

We prove that the fermionic Laughlin V_(1) Hamiltonian at filling 1/3 on expanding round spheres retains a unique ground state and a uniform spectral gap under sufficiently weak bounded real scalar one-body potentials projected to the lowest Landau level. With coefficient one for each pair projector and Laughlin flux q=3(N-1), the gap and perturbation threshold are uniform for all sufficiently large particle numbers and all potential profiles of supremum norm at most one. The result uses the uniform unperturbed Fock-space gap and gives existential constants.

We prove the spherical fermionic Laughlin spectral-gap conjecture for the full V_(1) interaction. With coefficient one for each pair projector, the gap above the Laughlin state at filling 1/3 on the round sphere is at least 1/25 for all sufficiently large systems. More generally, H_Q^2≥\gamma H_Q for some fixed \gamma> 1/25 on the entire lowest-Landau-level Fock space for all sufficiently large flux Q, independently of particle number.