{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"00db496308ea0359289ee2f20acc51b7414eaf8279424e87557c60b72331ab37","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"66c58f57ac3ad656e0b7c42f57e18a1f678c1901d3fe130df9c35c93fada917a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.quantum-spin-gaps.aklt-square","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The AKLT model is a specially designed quantum magnet whose ground state is known exactly. Its energy gap is proven in one dimension and on the honeycomb lattice but not on the square lattice.","posed_since":"1987","precise":"Spin-2 AKLT model on $Z^{2}$: H = sum_<ij> P^(4)_{ij}, with P^(4) the projector onto total spin 4 of a nearest-neighbour pair. Prove that the gap above the unique ground state is bounded below uniformly in system size. Answer: a proof, possibly via a finite-size criterion checked by computer.","problem_ref":null,"references":"","settled_by":"A finite-size gap criterion verified numerically with rigorous error control, or an analytic proof.","status_note":"Gaps are proven on the hexagonal lattice (Lemm, Sandvik and Wang; Pomata and Wei, 2019-2020) and on decorated square lattices (2019), extended to generalized decorated graphs (Lucia and Young, 2023) and other spin-2 lattices (Guo, Pomata and Wei, 2021); the undecorated square lattice remains unproven.","title":"Spectral gap of the AKLT model on the square 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