A boundary-field gap for the spin-one Heisenberg chain

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.