Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement

• URL: http://arxiv.org/abs/2504.10569v1
• Date: Mon, 14 Apr 2025 18:00:00 GMT
• Title: Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement
• Authors: Po-Shen Hsin, Ryohei Kobayashi, Abhinav Prem,
• Abstract summary: 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.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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