Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases
In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, 0, Z[subscript 2], or Z. For example, noninteracting one-dimensional fermionic superconducting phases with S[subscript z] spin rotation and time-r...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/73874 https://orcid.org/0000-0002-9366-7925 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1811078377012985856 |
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| author | Tang, Evelyn May Yin Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Tang, Evelyn May Yin Wen, Xiao-Gang |
| author_sort | Tang, Evelyn May Yin |
| collection | MIT |
| description | In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, 0, Z[subscript 2], or Z. For example, noninteracting one-dimensional fermionic superconducting phases with S[subscript z] spin rotation and time-reversal symmetries are classified by Z. We show that with weak interactions, this classification reduces to Z[subscript 4]. Using group cohomology, one can additionally show that there are only four distinct phases for such one-dimensional superconductors even with strong interactions. Comparing their projective representations, we find that all these four symmetry-protected topological phases can be realized with free fermions. Further, we show that one-dimensional fermionic superconducting phases with Z[subscript n] discrete S[subscript z] spin rotation and time-reversal symmetries are classified by Z[subscript 4] when n is even and Z[subscript 2] when n is odd; again, all these strongly interacting topological phases can be realized by noninteracting fermions. Our approach can be applied to systems with other symmetries to see which one-dimensional topological phases can be realized with free fermions. |
| first_indexed | 2024-09-23T10:58:32Z |
| format | Article |
| id | mit-1721.1/73874 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:58:32Z |
| publishDate | 2012 |
| publisher | American Physical Society |
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| spelling | mit-1721.1/738742022-10-01T00:19:58Z Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases Tang, Evelyn May Yin Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Tang, Evelyn May Yin Wen, Xiao-Gang In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, 0, Z[subscript 2], or Z. For example, noninteracting one-dimensional fermionic superconducting phases with S[subscript z] spin rotation and time-reversal symmetries are classified by Z. We show that with weak interactions, this classification reduces to Z[subscript 4]. Using group cohomology, one can additionally show that there are only four distinct phases for such one-dimensional superconductors even with strong interactions. Comparing their projective representations, we find that all these four symmetry-protected topological phases can be realized with free fermions. Further, we show that one-dimensional fermionic superconducting phases with Z[subscript n] discrete S[subscript z] spin rotation and time-reversal symmetries are classified by Z[subscript 4] when n is even and Z[subscript 2] when n is odd; again, all these strongly interacting topological phases can be realized by noninteracting fermions. Our approach can be applied to systems with other symmetries to see which one-dimensional topological phases can be realized with free fermions. National Science Foundation (U.S.) (Grant DMR-1005541) National Science Foundation (U.S.) (Grant 11074140) 2012-10-10T20:53:41Z 2012-10-10T20:53:41Z 2012-08 2012-05 Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/73874 Tang, Evelyn, and Xiao-Gang Wen. “Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases.” Physical Review Letters 109.9 (2012). © 2012 American Physical Society https://orcid.org/0000-0002-9366-7925 https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevLett.109.096403 Physical Review Letters 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 APS |
| spellingShingle | Tang, Evelyn May Yin Wen, Xiao-Gang Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases |
| title | Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases |
| title_full | Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases |
| title_fullStr | Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases |
| title_full_unstemmed | Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases |
| title_short | Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases |
| title_sort | interacting one dimensional fermionic symmetry protected topological phases |
| url | http://hdl.handle.net/1721.1/73874 https://orcid.org/0000-0002-9366-7925 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT tangevelynmayyin interactingonedimensionalfermionicsymmetryprotectedtopologicalphases AT wenxiaogang interactingonedimensionalfermionicsymmetryprotectedtopologicalphases |