{"id":"openai-math/The-periodic-spin-one-Haldane-gap","pdf":"https://github.com/openai/math/blob/main/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026","tags":["quantum-spin-chains","condensed-matter","spectral-gap"],"score":0,"title":"The periodic spin-one Haldane gap","domain":"Mathematical physics","family":"268","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove a uniform positive spectral gap for the pure antiferromagnetic spin-one Heisenberg chain on even periodic rings, establishing the positive even-periodic formulation of the spin-one Haldane conjecture.","category":"research","comments":1,"disputed":false,"division":"math","mentions":0,"discussed":5,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://haltasaki.github.io/writings/AI/OpenAI_Haldane.html","kind":"web","site":"haltasaki.github.io","text":"Two expository notes by Hal Tasaki on the analytic argument in OpenAI's proof of the periodic spin-one Haldane gap: continuous-time and discrete-time versions.","added":"2026-11-03","title":"OpenAI's proof of the Haldane gap in the S=1 antiferromagnetic Heisenberg chain","author":"Hal Tasaki"},{"url":"https://online.kitp.ucsb.edu/online/physicsai-m26/lu/#:~:text=Bridging%20Gaps%20with%20Tensor%20Networks","kind":"web","site":"online.kitp.ucsb.edu","text":"Bridging Gaps with Tensor Networks: The Haldane Gap Proof and Beyond Schedule Oct 20, 2026 Bridging Gaps with Tensor Networks: The Haldane Gap Proof and Beyond Sirui Lu (MPQ) To download: Right-click and choose \"Save Link As...\"","added":"2026-11-04","title":"Sirui Lu (MPQ), Bridging Gaps with Tensor Networks: The Haldane Gap Proof and Beyond","author":"Sirui Lu (MPQ)"},{"url":"https://x.com/MasakiOshikawa/status/2107609927351177678","date":"2026-10-06","kind":"x","added":"2026-11-03","author":"Masaki Oshikawa (押川 正毅)","handle":"MasakiOshikawa"},{"url":"https://x.com/ryuikaneko/status/2107660763020267941","date":"2026-10-07","kind":"x","added":"2026-11-03","author":"Ryui Kaneko","handle":"ryuikaneko"},{"url":"https://x.com/Hal_Tasaki/status/2109159859845472457","date":"2026-10-11","kind":"x","added":"2026-11-03","author":"Hal Tasaki","handle":"Hal_Tasaki"}],"formalized":false,"family_title":"The spin-one Haldane gap"}