Detecting Quantum Anomalies in Open Systems,Physical Review Letters

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Detecting Quantum Anomalies in Open Systems
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-05 , DOI: 10.1103/physrevlett.133.106503
Yunlong Zang _{1,

2} , Yingfei Gu ₃ , Shenghan Jiang _{1,

2}

Affiliation

Symmetries and quantum anomalies serve as powerful tools for constraining complicated quantum many-body systems, offering valuable insights into low-energy characteristics based on their ultraviolet structure. Nevertheless, their applicability has traditionally been confined to closed quantum systems, rendering them largely unexplored for open quantum systems described by density matrices. In this Letter, we introduce a novel and experimentally feasible approach to detect quantum anomalies in open systems. Specifically, we claim that, when coupled with an external environment, the mixed ’t Hooft anomaly between spin rotation symmetry and lattice translation symmetry gives distinctive characteristics for half-integer and integer spin chains in measurements of

\exp (i θ S_{tot}^{z})

as a function of

θ

. Notably, the half-integer spin chain manifests a topological phenomenon akin to the “level crossing” observed in closed systems. To substantiate our assertion, we develop a lattice-level spacetime rotation to analyze the aforementioned measurements. Based on the matrix product density operator and transfer matrix formalism, we analytically establish and numerically demonstrate the unavoidable singular behavior of

\exp (i θ S_{tot}^{z})

for half-integer spin chains. Conceptually, our work demonstrates a way to discuss notions like “spectral flow” and “flux threading” in open systems not necessarily with a Hamiltonian.

中文翻译：

检测开放系统中的量子异常

对称性和量子异常是约束复杂量子多体系统的强大工具，为基于其紫外线结构的低能量特性提供了宝贵的见解。然而，它们的适用性传统上仅限于封闭量子系统，这使得它们在很大程度上尚未被探索用于密度矩阵描述的开放量子系统。在这封信中，我们介绍了一种新颖且实验上可行的方法来检测开放系统中的量子异常。具体来说，我们声称，当与外部环境耦合时，自旋旋转对称性和晶格平移对称性之间的混合't Hooft异常在测量中为半整数和整数自旋链提供了独特的特征