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arXiv:1705.07868 · Physical review. B./Physical review. B

Exact zero modes in frustrated Haldane chains

Natalia Chepiga, Frédéric Mila

Published Aug 24, 2017• 10 citations
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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 ${J}_{1}\ensuremath{-}{J}_{2}$ model with nearest- and next-nearest-neighbor antiferromagnetic interactions, we show that the effective coupling in a chain of length $L$ changes sign $N\ensuremath{\simeq}0.38L$ times in the window $0.28\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.75$ 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.

DOI
10.1103/physrevb.96.060409

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We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S1>S2,{S}_{1}>{S}_{2},S1​>S2​, using 1/S1/S1/S spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
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