Anomaly in open quantum systems and its implications on mixed-state quantum phases

Understand

In this paper, we develop a systematic approach to characterize the 't Hooft anomaly in open quantum systems.

• Owing to nontrivial couplings to the environment, symmetries in such systems manifest as either strong or weak type.
• By representing their symmetry transformation through superoperators, we incorporate them in a unified framework that enables a direct calculation of their anomalies.
• In the case where the full symmetry group is $K\times G$, with $K$ the strong symmetry and $G$ the weak symmetry, we find that anomalies of bosonic systems are classified by $H^{d+2}(K\times G,U(1))/H^{d+2}(G,U(1))$ in $d$ spatial dimensions.