准周期自旋链中的拓扑间隙：数值与 K-理论分析
Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
AI总结：
本文结合数值与K-理论方法，证明准周期自旋链的Hamiltonian算子代数为非交换环面，展现出类量子霍尔效应，并揭示了相互作用对混合拓扑边缘模式的强烈影响，为利用phason实现选择性量子化磁化比特的拓扑自旋泵浦奠定了基础。
摘要：
本文通过数值和 K-理论方法研究了准周期自旋链模型支持的拓扑相及其体-边界原理。我们证明，对于非关联相和关联相，生成 Hamiltonian 的算子代数均是非交换环面，因此准周期链展现出类似于二维及更高维量子霍尔效应的物理现象。研究发现，稳健的拓扑边缘模式受到相互作用的强烈影响，并且通常具有边缘局域化与链退局域化相混合的结构。我们的发现为利用准周期模式的 phason 作为绝热参数进行拓扑自旋泵浦奠定了基础，在此过程中，选择性设定的量子化磁化比特可以从链的一端转移到另一端。
英文摘要：
Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras that generate the Hamiltonians are non-commutative tori, hence the quasi-periodic chains display physics akin to the quantum Hall effect in two and higher dimensions. The robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. Our findings lay the foundations for topological spin pumping using the phason of a quasi-periodic pattern as an adiabatic parameter, where selectively chosen quantized bits of magnetization can be transferred from one edge of the chain to the other.
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