{"id":"openai-math/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain","pdf":"https://github.com/openai/math/blob/main/preprints/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026","tags":["spin-chains","quantum-many-body","spectral-gap","mathematical-physics"],"score":0,"title":"A boundary-field gap for the spin-one Heisenberg chain","domain":"Mathematical physics","family":"268","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove a uniform spectral gap for odd open spin-one antiferromagnetic Heisenberg chains with the same fixed magnetic field at both endpoints. The field $`h=3/5`$ gives a gap greater than $`\\log(10)/392`$ on every chain of $`2L+1`$ sites with L ≥ 960. Tasaki's index theorem then gives index −1 for every subsequential local limit of these boundary-selected ground states.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The spin-one Haldane gap"}