Wave functions of bosonic symmetry protected topological phases
We study the structure of the ground-state wave functions of bosonic symmetry protected topological (SPT) insulators in three space dimensions. We demonstrate that the differences with conventional insulators are captured simply in a dual vortex description. As an example, we show that a previously...
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| Format: | Article |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/89161 https://orcid.org/0000-0003-4203-4148 |
| _version_ | 1811078271297650688 |
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| author | Xu, Cenke Todadri, Senthil |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Xu, Cenke Todadri, Senthil |
| author_sort | Xu, Cenke |
| collection | MIT |
| description | We study the structure of the ground-state wave functions of bosonic symmetry protected topological (SPT) insulators in three space dimensions. We demonstrate that the differences with conventional insulators are captured simply in a dual vortex description. As an example, we show that a previously studied bosonic topological insulator with both global U(1) and time-reversal symmetry can be described by a rather simple wave function written in terms of dual “vortex ribbons.” The wave function is a superposition of all the vortex-ribbon configurations of the boson, and a factor (−1) is associated with each self-linking of the vortex ribbons. This wave function can be conveniently derived using an effective field theory of the SPT phase in the strong-coupling limit, and it naturally explains all the phenomena of this SPT phase discussed previously. The ground-state structure for other three-dimensional (3D) bosonic SPT phases are also discussed similarly in terms of vortex loop gas wave functions. We show that our methods reproduce known results on the ground-state structure of some 2D SPT phases. |
| first_indexed | 2024-09-23T10:56:49Z |
| format | Article |
| id | mit-1721.1/89161 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:56:49Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/891612022-10-01T00:07:13Z Wave functions of bosonic symmetry protected topological phases Xu, Cenke Todadri, Senthil Massachusetts Institute of Technology. Department of Physics Todadri, Senthil We study the structure of the ground-state wave functions of bosonic symmetry protected topological (SPT) insulators in three space dimensions. We demonstrate that the differences with conventional insulators are captured simply in a dual vortex description. As an example, we show that a previously studied bosonic topological insulator with both global U(1) and time-reversal symmetry can be described by a rather simple wave function written in terms of dual “vortex ribbons.” The wave function is a superposition of all the vortex-ribbon configurations of the boson, and a factor (−1) is associated with each self-linking of the vortex ribbons. This wave function can be conveniently derived using an effective field theory of the SPT phase in the strong-coupling limit, and it naturally explains all the phenomena of this SPT phase discussed previously. The ground-state structure for other three-dimensional (3D) bosonic SPT phases are also discussed similarly in terms of vortex loop gas wave functions. We show that our methods reproduce known results on the ground-state structure of some 2D SPT phases. Alfred P. Sloan Foundation David & Lucile Packard Foundation Hellman Family Foundation National Science Foundation (U.S.) (NSF Grant No. DMR-1151208) National Science Foundation (U.S.) (NSF Grant No. DMR-1005434) Simons Foundation (Award No. 229736) 2014-09-03T19:24:21Z 2014-09-03T19:24:21Z 2013-05 2013-01 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/89161 Xu, Cenke, and Senthil Todadri. “Wave Functions of Bosonic Symmetry Protected Topological Phases.” Phys. Rev. B 87, no. 17 (May 2013). ©2013 American Physical Society. https://orcid.org/0000-0003-4203-4148 en_US http://dx.doi.org/10.1103/PhysRevB.87.174412 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society American Physical Society |
| spellingShingle | Xu, Cenke Todadri, Senthil Wave functions of bosonic symmetry protected topological phases |
| title | Wave functions of bosonic symmetry protected topological phases |
| title_full | Wave functions of bosonic symmetry protected topological phases |
| title_fullStr | Wave functions of bosonic symmetry protected topological phases |
| title_full_unstemmed | Wave functions of bosonic symmetry protected topological phases |
| title_short | Wave functions of bosonic symmetry protected topological phases |
| title_sort | wave functions of bosonic symmetry protected topological phases |
| url | http://hdl.handle.net/1721.1/89161 https://orcid.org/0000-0003-4203-4148 |
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