AI 中文总结
该研究从时空对偶视角，将量子通道的Liouvillian映射为高维mSPT相，引入TRNC作为时间关联探针，发现Liouvillian奇异谱可诊断量子异常。
AI 中文摘要
量子异常对多体系统的可能行为具有强约束作用，典型例子是Lieb-Schultz-Mattis（LSM）定理，它将紫外对称性与填充约束和能谱、基态结构的红外特征关联起来。本文探究LSM约束如何塑造开放量子系统的动力学特征与时间关联，利用时空对偶性，证明具有强S与弱G对称性混合异常的d维重复量子通道的Liouvillian，可映射为(d+1)维混合态对称性保护拓扑（mSPT）相；在该对应关系下，通道的初态与稳态被识别为体投影存在时高维mSPT的边界态。进一步引入扭曲Renyi-N关联函数（TRNC）作为通道时间关联的探针，证明其与mSPT奇异关联函数对偶，为诊断LSM异常隐含的长程时间序提供直接的体-边界路径。最终确定Liouvillian奇异谱（而非Liouvillian谱本身）是量子异常更基础的诊断工具，且其与mSPT的算子纠缠谱对偶。
英文摘要
Quantum anomalies strongly constrain the possible behavior of many-body systems. A prime example is the Lieb-Schultz-Mattis (LSM) theorem, which relates UV symmetry and filling constraints to IR features of the energy spectrum and ground-state structure. Here, we ask how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems. Using a spacetime duality, we show that the Liouvillian of a $d$-dimensional repeated quantum channel with a mixed anomaly between strong $S$ and weak $G$ symmetry can be mapped to a $(d{+}1)$-dimensional mixed-state symmetry-protected topological (mSPT) phase. Under this correspondence, the initial and steady states of the channel are identified with boundary states of the higher-dimensional mSPT in the presence of bulk projection. We further introduce the twisted Renyi-$N$ correlator (TRNC) as a probe of temporal correlations in the channel and demonstrate that it is dual to the mSPT strange correlator, providing a direct bulk-boundary route to diagnose long-range temporal order implied by the LSM anomaly. Finally, we identify the \textit{Liouvillian singular spectrum}, rather than the Liouvillian spectrum itself, as a more fundamental diagnostic of quantum anomalies, and show that it is dual to the operator entanglement spectrum of the mSPT.
