Laughlin bulk spectral gap
For the full fermionic Haldane pseudopotential projected to the lowest Landau level on tori with fixed magnetic length and bounded aspect ratio, prove a system-size-independent positive energy gap above its ground space at .
Problem statement
For the full fermionic Haldane pseudopotential projected to the lowest Landau level on tori with fixed magnetic length and bounded aspect ratio, prove a system-size-independent positive energy gap above its ground space at .
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
The energy normalization is fixed as particle number grows. The target is the untruncated parent Hamiltonian in the two-dimensional thermodynamic limit, not a thin-cylinder approximation and not uniqueness of a topologically degenerate ground space.
Established baseline: Warzel and Young prove a gap for a thin-torus truncated model. That important theorem does not establish the full pseudopotential gap on bounded-aspect-ratio tori.
Preprint progress (2026): Schraven and Warzel study thin-cylinder Laughlin correlations and an entanglement-spectrum gap. An entanglement-spectrum gap is not the Hamiltonian excitation gap sought here. Rigorous finite-size criteria or controlled approximation errors connecting a solved model to the full parent would be meaningful partial progress.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
preprint: Thin-cylinder correlation decay and an entanglement-spectrum gap; not a proof of the full bulk energy gap. Evidence
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
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Discussion
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