The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.

中文翻译：

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分段自旋的拓扑量子同步

Affleck-Kennedy-Lieb-Tasaki 模型的带隙对称相在开链末端表现出分段自旋。我们证明，打破 SU(2) 对称性并应用全局自旋降低耗散器可以实现这些分段自旋的同步。额外的局部耗散器确保收敛到基态流形。为了了解这种同步的哪些方面在整个 Haldane 间隙相中是稳健的，我们减少了双二次项，这消除了对外部场的需要，但会破坏同步的稳定性。在基态子空间内，仅使用全局降低耗散器即可恢复稳定性。这些结果表明，分段自由度可以在扩展系统中同步，并具有拓扑保护带来的显着鲁棒性。直接的结果是，动态同步不需要排列对称性，这与排列对称性引起的同步相比，代表了拓扑同步的明显优势。