12:30 pm MCP - 3rd Floor Atrium
Decohered but entangled: how symmetries and anomalies constrain mixed states.
Symmetries and their anomalies are among the most powerful non-perturbative tools to characterize quantum many-body systems. However, they have been traditionally applied to closed systems and pure states. In this talk, I discuss how symmetry-based constraints extend to open systems and mixed states. First, we show that topological order — viewed as a strong, anomalous 1-form symmetry in (2 + 1)-D — can survive as a long-range–entangled phase of matter even for mixed states. Second, we address 0-form anomalies, which can appear at the boundary of SPT phases. There, we prove that strongly symmetric anomalous states exhibit long-range multipartite entanglement. Curiously, we find intrinsically mixed phases in (1 + 1)-D with states possessing tripartite entanglement but no bipartite entanglement. Finally, we analyze on-site symmetries. Even though they are not anomalous, we find that their maximally mixed states (MMSs) within a symmetric sector can still be highly entangled if the symmetry is non-Abelian, with logarithmic scaling of entanglement for non-Abelian Lie groups. To motivate the study of such states, we prove that the MMSs are the steady states of generic unital evolutions that preserve the system’s symmetry.