Journal article

Exact zero modes in frustrated Haldane chains

We show that the effective coupling between the spin-1/2 edge states of a spin-1 chain of finite length can be continuously tuned by frustration. For the J(1)-J(2) model with nearest-and next-nearest-neighbor antiferromagnetic interactions, we show that the effective coupling in a chain of length L changes sign N similar or equal to 0.38L times in the window 0.28 less than or similar to J(2)/J(1) less than or similar to 0.75 where the short-range correlations are incommensurate. This implies that there are N zero modes where the singlet and the triplet are strictly degenerate, i.e., N values of J(2)/J(1) where the spin-1/2 edge states are completely decoupled. We argue that this effect must be generic for all incommensurate phases with localized edge states, and we briefly discuss a few experimental implications.


Related material