OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
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=3/5 and gives boundary-selected infinite-volume states with topological index −1.
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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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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…
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.
This exact PDF is not listed in the imported formalization catalogue. Family scope notes may contain further information.
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