不可约映射的连通分支与一维量子相位
Connected components of irreducible maps and 1D quantum phases
摘要：
我们研究了量子Perron-Frobenius理论中出现的完全正（CP）映射集的基本拓扑性质。证明了具有固定Kraus秩的本原CP映射集是路连通的，并给出了在给定Kraus秩和固定周边谱下不可约CP映射的连通分支的重数分类.这些研究结果，然后应用于分析1D量子相位通过研究等价类的平移不变矩阵产品状态，对应于相应的CP映射的连接组件。我们的研究结果扩展了以前获得的图片，因为它们不需要阻塞的物理站点，他们导致分析路径，他们允许分解成遍历组件和研究打破平移对称性。
英文摘要：
We investigate elementary topological properties of sets of completely positive (CP) maps that arise in quantum Perron-Frobenius theory. We prove that the set of primitive CP maps of fixed Kraus rank is path-connected and we provide a complete classification of the connected components of irreducible CP maps at given Kraus rank and fixed peripheral spectrum in terms of a multiplicity index. These findings are then applied to analyse 1D quantum phases by studying equivalence classes of translational invariant Matrix Product States that correspond to the connected components of the respective CP maps. Our results extend the previously obtained picture in that they do not require blocking of physical sites, they lead to analytic paths and they allow to decompose into ergodic components and to study the breaking of translational symmetry.
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