{"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":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The spin-one Haldane gap"}