标题： 高阶异常意味着固有长程纠缠 显示英文标题

标题： Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement

摘要： 我们证明了那些尊重异常有限高阶对称性的通用能隙量子多体态与任何短程纠缠（SRE）态之间的重叠指数级小。因此，高阶对称性的异常强制产生$intrinsic$长程纠缠，这与普通（0阶）对称性的异常不同，后者与对称的SRE态相容（具体来说，是对称的猫态）。作为应用，我们表明强高阶对称性的异常为$d \geq 2$空间维数中的混合态拓扑序提供了一个诊断工具。我们还识别出一种新的（3+1）D内在混合态拓扑序，它不满足通过（3+1）D拓扑码中费米子环激发的局部退相干来远程检测。这种远程可检测性的破坏，如强高阶对称性异常所编码的，为内在混合态拓扑序提供了部分表征。 显示英文摘要

摘要： 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.