2025/04/14 by Hsin, Po-Shen, Kobayashi, Ryohei, Prem, Abhinav · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2504.10569
We show that generic gapped quantum many-body states which respect an anomalous finite higher-form symmetry have an exponentially small overlap with any short-range entangled (SRE) state. Hence, anomalies of higher-form symmetries enforce intrinsic long-range entanglement, which is in contrast with anomalies of ordinary (0-form) symmetries which are compatible with symmetric SRE states (specifically, symmetric cat states). As an application, we show that the anomalies of strong higher-form symmetries provide a diagnostic for mixed-state topological order in d ≥ 2 spatial dimensions. We also identify a new (3+1)D intrinsic mixed-state topological order that does not obey remote-detectability by local decoherence of the (3+1)D Toric Code with fermionic loop excitations. This breakdown of remote detectability, as encoded in anomalies of strong higher-form symmetries, provides a partial characterization of intrinsically mixed-state topological order.