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Uniform Laughlin gap and stability under bounded scalar disorder
Proves the fermionic Laughlin spectral-gap conjecture for the full V interaction at filling 1/3 on the round sphere. The unique ground state remains uniformly gapped under sufficiently weak bounded real scalar one-body potentials projected to the lowest Landau level. Both the gap and disorder threshold are uniform over all sufficiently large particle numbers and all normalized potential profiles.
Manuscripts in this family · 2
Uniform Stability of the Spherical Laughlin Gap
Oct 5, 2026·uniform-stability-spherical-laughlin-gap.pdf
We prove that the fermionic Laughlin V 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 , 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.
A Fock-space inequality and the Laughlin spectral gap
Sep 24, 2026·A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdfLean
We prove the spherical fermionic Laughlin spectral-gap conjecture for the full V 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, for some fixed on the entire lowest-Landau-level Fock space for all sufficiently large flux Q, independently of particle number.