键耗散Kitaev链中的分辩非布洛赫拓扑与非局域纠缠动力学
Sector-resolved non-Bloch topology and nonlocal entanglement dynamics in a bond-dissipative Kitaev chain
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中文总结 AI 辅助
该研究在键耗散Kitaev链中揭示分辩非布洛赫体边对应关系，发现局域密度对扇区拓扑不敏感，还通过平衡增益损耗下的纠缠谱零事件恢复隐藏边界内容。
中文摘要 AI 辅助
耗散非厄米拓扑的核心特征是弛豫动力学追踪非布洛赫体边对应关系，这使得无能隙区域呈现代数衰减，有能隙相呈现指数衰减，从而局域可观测量可直接用于诊断拓扑。我们证明该对应关系在耗散拓扑超导体中会失效，此时局域可观测量无法识别其应解码的拓扑。通过采用第三量子化速动矩阵形式的键耗散二聚化Kitaev链，我们发现零化学势下，马约拉纳速动矩阵会分解为两个独立的非厄米 sector（扇区），每个扇区具有各自的广义布里渊区和非布洛赫绕数，由此揭示了分辩非布洛赫体边对应关系。局域密度是跨扇区协变量，弛豫速率为两个扇区速率之和，因此即使一个扇区无能隙且拓扑，局域密度仍对扇区不敏感。在平衡增益与损耗下，纯周期性边界Lindblad演化下纠缠谱的有限时间零事件逐扇区恢复了这一隐藏的边界内容，作为动力学不变量，无需物理上打开链即可返回开放边界的边界速动值。
英文摘要
A core characteristic of dissipative non-Hermitian topology is that the relaxation dynamics tracks the non-Bloch bulk-boundary correspondence, rendering an algebraic decay in the gapless regime and an exponential falloff in the gapped phase, so that local observables directly diagnose the topology. We show that this correspondence breaks down in a dissipative topological superconductor, where the local observables turn blind to the very topology they are expected to decipher. Via a bond-dissipative dimerized Kitaev chain in a third-quantized rapidity-matrix formulation, we find that at zero chemical potential the Majorana rapidity matrix decomposes into two independent non-Hermitian sectors, each with its own generalized Brillouin zone and non-Bloch winding number, thereby revealing a sector-resolved non-Bloch bulk-boundary correspondence. The local density is a cross-sector covariance and relaxes at the sum of the two sector rates, so it remains sector-blind even when one sector is gapless and topological. For balanced gain and loss, the finite-time zero events of the entanglement spectrum under purely periodic-boundary Lindblad evolution recover this hidden edge content sector by sector, serving as a dynamical invariant that returns the open-boundary edge rapidities without physically opening the chain.
