The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov–Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.

中文翻译：

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拓扑秩序、混合状态和开放系统

与纯量子态相比，混合态在拓扑量子物质中的作用鲜为人知。出现在纯态中的拓扑相的推广直到最近才在文献中受到关注。特别是，Uhlmann 对混合态的 Aharonov-Anandan 相的推广是否在量子系统的行为中起任何物理作用仍不清楚。我们从一般的角度分析混合状态的拓扑阶段及其不变性的鲁棒性。特别是，我们分析了这些阶段在具有周期性对称性的系统的行为中的作用，以及它们在保持其晶体对称性的环境的影响下的演化。