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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 and gives boundary-selected infinite-volume states with topological index −1.
Manuscripts in this family · 2
The periodic spin-one Haldane gap
Sep 24, 2026·paper.pdf
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.
A boundary-field gap for the spin-one Heisenberg chain
Sep 24, 2026·paper.pdf
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 gives a gap greater than on every chain of sites with L ≥ 960. Tasaki's index theorem then gives index −1 for every subsequential local limit of these boundary-selected ground states.