AI 中文总结
该研究从逾渗视角探究退相干诱导拓扑相变的微观机制，以色码、环面码为案例，引入QLTEN、EP分析，发现两类拓扑码对EP响应不同，普适微观描述仍具挑战。
AI 中文摘要
我们研究退相干诱导的拓扑有序态之间相变的微观机制。作为首个案例研究，我们利用拓扑纠缠 negativity（TEN）和与1-形式对称性相关的无序参数分析色码，将这些量分别解释为一维和零维单纯同调对象，并证明该相变可通过退相干逾渗理解。为解析其局域结构，我们引入准局域TEN（QLTEN），其可可视化局域拓扑性质的空间分布及退相干区域的增长。我们进一步引入爆炸逾渗（EP），此处对应抑制大退相干团簇形成的偏置退相干。作为第二个案例研究，我们考虑三角晶格上的环面码在外场型退相干下的情况。数值结果表明，QLTEN可准确捕捉希格斯区域的出现和逻辑量子比特的存活情况。尽管两种模型中全局TEN、QLTEN团簇与弦算子高度相关，但色码与环面码对EP模式的响应不同，这表明即使对于密切相关的系统，退相干诱导拓扑相变的普适微观描述仍具挑战性。
英文摘要
We investigate microscopic mechanisms underlying decoherence-induced transitions between topologically ordered states. As a first case study, we analyze the color code using topological entanglement negativity (TEN) and a disorder parameter associated with 1-form symmetry. We interpret these quantities as first- and zeroth-dimensional simplicial homological objects, respectively, and show that the transition can be understood in terms of decoherence percolation. To resolve its local structure, we introduce quasi-local TEN (QLTEN), which visualizes the spatial distribution of local topological properties and the growth of decohered regions. We further introduce explosive percolation (EP), corresponding here to biased decoherence that suppresses the formation of large decohered clusters. As a second case study, we consider the toric code on a triangular lattice under external-field-type decoherence. Numerical results show that QLTEN faithfully captures the emergence of Higgs regions and the survival of logical qubits. Although global TEN, QLTEN clusters, and string operators are strongly correlated in both models, the color code and toric code respond differently to EP patterns. This difference indicates that a universal microscopic description of decoherence-induced topological phase transitions remains challenging even for closely related systems.
Comments21 pages, 19 main figures and 2 figures in Appendix. Revised version submitted to Physical Review B
