Twisted gauge theory model of topological phases in three dimensions
We propose an exactly solvable lattice Hamiltonian model of topological phases in 3+1 dimensions, based on a generic finite group G and a 4-cocycle ω over G. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-tor...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/97636 https://orcid.org/0000-0001-5742-3395 |
| _version_ | 1826209908857503744 |
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| author | Wan, Yidun He, Huan Wang, Juven |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Wan, Yidun He, Huan Wang, Juven |
| author_sort | Wan, Yidun |
| collection | MIT |
| description | We propose an exactly solvable lattice Hamiltonian model of topological phases in 3+1 dimensions, based on a generic finite group G and a 4-cocycle ω over G. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasiexcitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the SL(3,Z) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ω and quantities derived from ω. Our model fulfills a Hamiltonian extension of the (3+1)-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G. This work is presented to be accessible for a wide range of physicists and mathematicians. |
| first_indexed | 2024-09-23T14:34:54Z |
| format | Article |
| id | mit-1721.1/97636 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:34:54Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/976362022-10-01T21:44:40Z Twisted gauge theory model of topological phases in three dimensions Wan, Yidun He, Huan Wang, Juven Massachusetts Institute of Technology. Department of Physics Wang, Juven We propose an exactly solvable lattice Hamiltonian model of topological phases in 3+1 dimensions, based on a generic finite group G and a 4-cocycle ω over G. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasiexcitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the SL(3,Z) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ω and quantities derived from ω. Our model fulfills a Hamiltonian extension of the (3+1)-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G. This work is presented to be accessible for a wide range of physicists and mathematicians. Perimeter Institute for Theoretical Physics National Science Foundation (U.S.) (Grant DMR-1005541) National Natural Science Foundation (China) (Grant 11074140) National Natural Science Foundation (China) (Grant 11274192) BMO Financial Group Templeton Foundation 2015-07-02T14:29:03Z 2015-07-02T14:29:03Z 2015-07 2015-05 2015-07-01T22:00:05Z Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/97636 Wan, Yidun, Juven C. Wang, and Huan He. "Twisted gauge theory model of topological phases in three dimensions." Phys. Rev. B 92, 045101 (July 2015). © 2015 American Physical Society https://orcid.org/0000-0001-5742-3395 en http://dx.doi.org/10.1103/PhysRevB.92.045101 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Wan, Yidun He, Huan Wang, Juven Twisted gauge theory model of topological phases in three dimensions |
| title | Twisted gauge theory model of topological phases in three dimensions |
| title_full | Twisted gauge theory model of topological phases in three dimensions |
| title_fullStr | Twisted gauge theory model of topological phases in three dimensions |
| title_full_unstemmed | Twisted gauge theory model of topological phases in three dimensions |
| title_short | Twisted gauge theory model of topological phases in three dimensions |
| title_sort | twisted gauge theory model of topological phases in three dimensions |
| url | http://hdl.handle.net/1721.1/97636 https://orcid.org/0000-0001-5742-3395 |
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