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Article: Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries
Title | Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries |
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Authors | |
Issue Date | 2021 |
Publisher | American Physical Society. The Journal's web site is located at http://journals.aps.org/prb/ |
Citation | Physical Review B: covering condensed matter and materials physics, 2021, v. 104 n. 7, p. article no. 075111 How to Cite? |
Abstract | We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric, and topologically ordered, i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of U(1), SU(2), or SO(3). In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous tenfold-way classification, with the time-reversal symmetry replaced by the mirror symmetry and with strong interaction taken into account. For surface SETs, the most general interplay between symmetries and anyon excitations is considered. Based on the previously proposed dimensional reduction and folding approaches, we rederive the classification of bulk SPT phases and define a complete set of bulk topological invariants for every symmetry group under consideration and then derive explicit expressions of the bulk invariants in terms of surface topological properties (such as topological spin, quantum dimension) and symmetry properties (such as mirror fractionalization, fractional charge or spin). These expressions are our quantitative bulk-boundary correspondences. Meanwhile, the bulk topological invariants can be interpreted as anomaly indicators for the surface SETs which carry 't Hooft anomalies of the associated symmetries whenever the bulk is topologically nontrivial. Hence, the quantitative bulk-boundary correspondences provide an easy way to compute the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators are complete. Our derivations of the bulk-boundary correspondences and anomaly indicators are explicit and physically transparent. The anomaly indicators obtained in this work can be straightforwardly translated to their time-reversal counterparts that apply to the usual topological insulators and topological superconductors, due to a known correspondence between mirror and time-reversal topological phases. |
Persistent Identifier | http://hdl.handle.net/10722/302086 |
ISSN | 2023 Impact Factor: 3.2 2023 SCImago Journal Rankings: 1.345 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ning, SQ | - |
dc.contributor.author | Mao, BB | - |
dc.contributor.author | LI, Z | - |
dc.contributor.author | Wang, C | - |
dc.date.accessioned | 2021-08-21T03:31:22Z | - |
dc.date.available | 2021-08-21T03:31:22Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Physical Review B: covering condensed matter and materials physics, 2021, v. 104 n. 7, p. article no. 075111 | - |
dc.identifier.issn | 2469-9950 | - |
dc.identifier.uri | http://hdl.handle.net/10722/302086 | - |
dc.description.abstract | We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric, and topologically ordered, i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of U(1), SU(2), or SO(3). In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous tenfold-way classification, with the time-reversal symmetry replaced by the mirror symmetry and with strong interaction taken into account. For surface SETs, the most general interplay between symmetries and anyon excitations is considered. Based on the previously proposed dimensional reduction and folding approaches, we rederive the classification of bulk SPT phases and define a complete set of bulk topological invariants for every symmetry group under consideration and then derive explicit expressions of the bulk invariants in terms of surface topological properties (such as topological spin, quantum dimension) and symmetry properties (such as mirror fractionalization, fractional charge or spin). These expressions are our quantitative bulk-boundary correspondences. Meanwhile, the bulk topological invariants can be interpreted as anomaly indicators for the surface SETs which carry 't Hooft anomalies of the associated symmetries whenever the bulk is topologically nontrivial. Hence, the quantitative bulk-boundary correspondences provide an easy way to compute the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators are complete. Our derivations of the bulk-boundary correspondences and anomaly indicators are explicit and physically transparent. The anomaly indicators obtained in this work can be straightforwardly translated to their time-reversal counterparts that apply to the usual topological insulators and topological superconductors, due to a known correspondence between mirror and time-reversal topological phases. | - |
dc.language | eng | - |
dc.publisher | American Physical Society. The Journal's web site is located at http://journals.aps.org/prb/ | - |
dc.relation.ispartof | Physical Review B: covering condensed matter and materials physics | - |
dc.rights | Copyright [2021] by The American Physical Society. This article is available online at [http://dx.doi.org/10.1103/PhysRevB.104.075111]. | - |
dc.title | Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries | - |
dc.type | Article | - |
dc.identifier.email | Ning, SQ: sqning91@hku.hk | - |
dc.identifier.email | Mao, BB: maobb@hku.hk | - |
dc.identifier.email | Wang, C: cjwang@hku.hk | - |
dc.identifier.authority | Wang, C=rp02502 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1103/PhysRevB.104.075111 | - |
dc.identifier.scopus | eid_2-s2.0-85113137860 | - |
dc.identifier.hkuros | 324471 | - |
dc.identifier.volume | 104 | - |
dc.identifier.issue | 7 | - |
dc.identifier.spage | article no. 075111 | - |
dc.identifier.epage | article no. 075111 | - |
dc.identifier.isi | WOS:000684135400001 | - |
dc.publisher.place | United States | - |