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arXiv · 2504.10569

Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement

Po-Shen Hsin·Ryohei Kobayashi·Abhinav Prem
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Abstract

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 $d \geq 2$ 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.

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Po-Shen Hsin, Ryohei Kobayashi, Abhinav Prem. 2025-04-14. Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement. https://arxiv.org/abs/2504.10569

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