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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2208.09001 |
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| _version_ | 1866916141780172800 |
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| author | Wen, Rui Potter, Andrew C. |
| author_facet | Wen, Rui Potter, Andrew C. |
| contents | Intrinsically gapless symmetry protected topological phases (igSPT) are gapless systems with SPT edge states with properties that could not arise in a gapped system with the same symmetry and dimensionality. igSPT states arise from gapless systems in which an anomaly in the low-energy (IR) symmetry group emerges from an extended anomaly-free microscopic (UV) symmetry We construct a general framework for constructing lattice models for igSPT phases with emergent anomalies classified by group cohomology, and establish a direct connection between the emergent anomaly, group-extension, and topological edge states by gauging the extending symmetry. In many examples, the edge-state protection has a physically transparent mechanism: the extending UV symmetry operations pump lower dimensional SPTs onto the igSPT edge, tuning the edge to a (multi)critical point between different SPTs protected by the IR symmetry. In two- and three- dimensional systems, an additional possibility is that the emergent anomaly can be satisfied by an anomalous symmetry-enriched topological order, which we call a quotient-symmetry enriched topological order (QSET) that is sharply distinguished from the non-anomalous UV SETs by an edge phase transition. We construct exactly solvable lattice models with QSET order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09001 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology Wen, Rui Potter, Andrew C. Strongly Correlated Electrons Quantum Physics Intrinsically gapless symmetry protected topological phases (igSPT) are gapless systems with SPT edge states with properties that could not arise in a gapped system with the same symmetry and dimensionality. igSPT states arise from gapless systems in which an anomaly in the low-energy (IR) symmetry group emerges from an extended anomaly-free microscopic (UV) symmetry We construct a general framework for constructing lattice models for igSPT phases with emergent anomalies classified by group cohomology, and establish a direct connection between the emergent anomaly, group-extension, and topological edge states by gauging the extending symmetry. In many examples, the edge-state protection has a physically transparent mechanism: the extending UV symmetry operations pump lower dimensional SPTs onto the igSPT edge, tuning the edge to a (multi)critical point between different SPTs protected by the IR symmetry. In two- and three- dimensional systems, an additional possibility is that the emergent anomaly can be satisfied by an anomalous symmetry-enriched topological order, which we call a quotient-symmetry enriched topological order (QSET) that is sharply distinguished from the non-anomalous UV SETs by an edge phase transition. We construct exactly solvable lattice models with QSET order. |
| title | Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2208.09001 |