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Speaker: Linhao Li
(Ghent University)


Abstract:: In this talk, I will introduce our recent work on how to characterize the 't Hooft anomalies in open quantum systems [1]. Owing to nontrivial couplings to the environment, symmetries in such systems manifest as either strong or weak type. The total symmetry \Gamma can fit into the symmetry extension: 1→K→\Gamma→G→1 with K the strong symmetry and G the weak symmetry. By representing their symmetry transformation through superoperators, we incorporate them in a unified framework that enables a direct calculation of their anomalies. We find that anomalies of bosonic systems are classified by $H^{d+2}(\Gamma,U(1))/H^{d+2}(G,U(1))$ in d spatial dimensions.  We  also generally prove that anomaly must lead to nontrivial mixed-state quantum phases as long as the weak symmetry is imposed, which can guarantee nontrivial steady states and long-time dynamics for open quantum systems governed by Lindbladians.  Finally, we explore the generalization of the ``anomaly inflow" mechanism in open quantum systems.Reference:[1] Zijian Wang, Linhao Li, arXiv: 2403.14533