Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums
Doubled topological phases introduced by Kitaev, Levin, and Wen supported on two-dimensional lattices are Hamiltonian versions of three-dimensional topological quantum field theories described by the Turaev-Viro state sum models. We introduce the latter with an emphasis on obtaining them from theori...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/671039 |
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| _version_ | 1832547017306406912 |
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| author | Zoltán Kádár Annalisa Marzuoli Mario Rasetti |
| author_facet | Zoltán Kádár Annalisa Marzuoli Mario Rasetti |
| author_sort | Zoltán Kádár |
| collection | DOAJ |
| description | Doubled topological phases introduced by Kitaev, Levin, and Wen supported on two-dimensional lattices are Hamiltonian versions of three-dimensional topological quantum field theories described by the Turaev-Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum. Equivalence of the previous models in the ground state is shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. An analysis of the ribbon operators describing excitations in both types of models and the three-dimensional geometrical interpretation are given. |
| format | Article |
| id | doaj-art-7298f44ae7af4cb58d6a6406baff1aa2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7298f44ae7af4cb58d6a6406baff1aa22025-02-03T06:46:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/671039671039Microscopic Description of 2D Topological Phases, Duality, and 3D State SumsZoltán Kádár0Annalisa Marzuoli1Mario Rasetti2Institute for Scientific Interchange Foundation, Villa Gualino, Viale Settimio Severo 75, 10131 Torino, ItalyInstitute for Scientific Interchange Foundation, Villa Gualino, Viale Settimio Severo 75, 10131 Torino, ItalyInstitute for Scientific Interchange Foundation, Villa Gualino, Viale Settimio Severo 75, 10131 Torino, ItalyDoubled topological phases introduced by Kitaev, Levin, and Wen supported on two-dimensional lattices are Hamiltonian versions of three-dimensional topological quantum field theories described by the Turaev-Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum. Equivalence of the previous models in the ground state is shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. An analysis of the ribbon operators describing excitations in both types of models and the three-dimensional geometrical interpretation are given.http://dx.doi.org/10.1155/2010/671039 |
| spellingShingle | Zoltán Kádár Annalisa Marzuoli Mario Rasetti Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums Advances in Mathematical Physics |
| title | Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums |
| title_full | Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums |
| title_fullStr | Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums |
| title_full_unstemmed | Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums |
| title_short | Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums |
| title_sort | microscopic description of 2d topological phases duality and 3d state sums |
| url | http://dx.doi.org/10.1155/2010/671039 |
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