A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases

Abstract

Symmetry-protected phases are gapped phases of matter which are distinguished only in the presence of a global symmetry G. These quantum phases lack any symmetry-breaking or topological order, and have short-range entangled ground states. Based on this short-range entanglement property, we give a general argument for the existence of an emergent unitary or anti-unitary ${\mathbb{Z}}_2$ symmetry at a critical point separating two different bosonic symmetry-protected phases in any dimension. Often, the emergent symmetry group at criticality has a mixed global anomaly. For those phases classified by group cohomology, we identify a criterion for when such a mixed global anomaly is present, and write down representative cocycles for the corresponding anomaly class. We illustrate our results with a series of examples, and make connections to recent results on (2 + 1)-d beyond-Landau critical points.

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• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Mixed-state quantum anomaly and multipartite entanglement
• Building models of topological quantum criticality from pivot Hamiltonians
• Duality viewpoint of criticality
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Many-body quantum catalysts for transforming between phases of matter
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle