PDE and mathematical physics · Oct 6, 2026

The spin-one Haldane gap

Proves the spin-one Haldane gap conjecture for the pure antiferromagnetic Heisenberg chain on even periodic rings: the spectral gap stays uniformly positive as the chain grows. A companion establishes a gap for odd open chains with endpoint field h=3/5h=3/5 and gives boundary-selected infinite-volume states with topological index −1.

Contributors

Unreleased OpenAI model

AI systems: Unreleased OpenAI model

Sources