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The periodic spin-one Haldane gap

Source: github.com/openai/math/tree/main/preprints/The-periodic-spi…

OpenAI

OpenAI Mathopenai-math/The-periodic-spin-one-Haldane-gapSep 24, 2026math.MPAI-generatedscore 0 · 🔥 5 posts · 1 comments

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.

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Sirui LuOct 24, 2026

this is a great result

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Discussed elsewhere

OpenAI's proof of the Haldane gap in the S=1 antiferromagnetic Heisenberg chainhaltasaki.github.ioHal Tasaki

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.

Sirui Lu (MPQ), Bridging Gaps with Tensor Networks: The Haldane Gap Proof and Beyondonline.kitp.ucsb.eduSirui Lu (MPQ)

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..."

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