Exact zero modes in frustrated Haldane chains

Abstract

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 $N\simeq 0.38L$ times in the window $0.28\lesssim J_2/J_1\lesssim 0.75$ 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.

5 pages, 6 figures. The last paragraph about experimental implications has been rewritten

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• Floating, critical and dimerized phases in a frustrated spin-3/2 chain
• Topological and quantum critical properties of the interacting Majorana chain model
• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Rigorous decoupling between edge states in frustrated spin chains and ladders
• Promising regimes for the observation of topological degeneracy in spin chains
• Perturbative approach to quantum tunneling and quantum interferences in spin clusters