标题： 开放量子系统中弱对称性的拓扑响应 显示英文标题

标题： Topological response in open quantum systems with weak symmetries

摘要： 在开放量子系统中，系统与环境的相互作用会产生两种类型的对称性：一种是强对称性，其中系统的对称电荷被精确地守恒；另一种是弱对称性，其中对称电荷可以与环境交换，但在平均意义上保持守恒。 虽然一般的开放量子系统仅具有弱对称性，但对于玻色子/自旋系统的对称性保护拓扑响应，仅在具有附加强对称性的严格设置中被考虑过。 在此，我们研究一般情况并证明，仅弱对称性就可以保护区分不同物质相的拓扑响应。 对于玻色子系统，聚焦于由局部可纯化密度算符描述的一维混合态，我们提出了一种量化响应，用于表征定性不同的相。 该响应可通过不同字符串序参数的衰减行为进行检测。 我们通过一个有噪声的Affleck-Kennedy-Lieb-Tasaki模型验证了我们的普遍结果。 特别是，我们展示了与环境的耦合可以诱导一种由弱对称性保护的状态相变，而这种相变没有纯态或强对称性的对应物。 显示英文摘要

摘要： In open quantum systems, the interaction of the system with its environment gives rise to two types of symmetry: a strong one, where the system's symmetry charge is conserved exactly, and a weak one, where the symmetry charge can be exchanged with the environment but remains conserved on average. While generic open quantum systems feature weak symmetries only, the symmetry protected topological response for bosonic/spin systems has only been considered in the stricter setup with additional strong symmetries. Here, we address the generic case and demonstrate that weak symmetries alone can protect topological responses that distinguish different phases of matter. For bosonic systems, focusing on one-dimensional mixed states described by locally purifiable density operators, we propose a quantized response characterizing qualitatively distinct phases. It is detectable via the decay behavior of different string order parameters. We validate our general results through a noisy Affleck-Kennedy-Lieb-Tasaki model. In particular, we show that the coupling to the environment can induce a phase transition to a state protected by weak symmetries, without a pure-state or strong-symmetry analog.