平均对称保护拓扑态在对称保持量子操作下的命运
Fate of average symmetry-protected topological states under symmetry-preserving quantum operations
- Graduate School of Engineering Science, Akita University（秋田大学工学研究科）
- Department of Physics, College of Humanities and Sciences, Nihon University（日本大学文理学部物理学科）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究一维团簇态的平均对称保护拓扑态在对称保持量子操作下的稳定性，发现其在广泛退相干和后选择强度下保持鲁棒，但在极限下出现强到弱或弱对称自发对称破缺。
AI中文摘要：
本文利用 Choi 映射，即加倍希尔伯特空间形式，研究基于一维团簇态的平均对称保护拓扑（ASPT）态的命运。通过在每条加倍的梯级上引入两个有效自旋 $τ$ 和 $η$，我们获得了 ASPT 母哈密顿量的透明表示，并系统地识别了守恒稳定子及相应的序。我们进一步结合定性有效哈密顿量和系统的母哈密顿量分析以及数值矩阵乘积态滤波计算，研究使 ASPT 变形的对称保持操作。我们发现，尽管 ASPT 在广泛的退相干强度范围内保持鲁棒性，但在最大退相干极限下，强到弱自发对称破缺（SWSSB）变得精确。此外，我们考虑了保持对称性的无点击后选择，这移除了支持 ASPT 的 Rényi-2 弦序的精确守恒律，并驱动系统走向弱对称自发对称破缺（WSSB）。同样，ASPT 在广泛的后选择强度范围内保持鲁棒性，WSSB 仅在投影极限附近变得显著，并在该极限处变得精确。
英文摘要：
The fate of average symmetry-protected topological (ASPT) states based on the one-dimensional cluster state is investigated by using the Choi mapping, namely, the doubled Hilbert-space formalism. By introducing two effective spins, $τ$ and $η$, on each doubled rung, we obtain a transparent representation of the ASPT parent Hamiltonian and systematically identify the conserved stabilizers and the corresponding orders. We further study symmetry-preserving operations that deform the ASPT by combining qualitative effective-Hamiltonian and systematic parent-Hamiltonian analyses with numerical matrix-product-state filtering calculations. We find that although the ASPT remains robust over a broad range of decoherence strengths, strong-to-weak spontaneous symmetry breaking (SWSSB) becomes exact in the maximal-decoherence limit. In addition, we consider symmetry preserving no-click postselection, which removes the exact conservation law supporting the Rényi-2 string order of the ASPT and drives the system toward weak-symmetry spontaneous symmetry breaking (WSSB). Again, the ASPT remains robust over a broad range of postselection strengths, with WSSB becoming pronounced only near the projective limit and exact at the limit itself.
