Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States
We propose a way—universal wave-function overlap—to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders...
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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/1721.1/97743 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826216811546279936 |
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| author | Moradi, Heidar Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Moradi, Heidar Wen, Xiao-Gang |
| author_sort | Moradi, Heidar |
| collection | MIT |
| description | We propose a way—universal wave-function overlap—to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M[superscript d]) of closed spatial manifold M[superscript d]. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations. |
| first_indexed | 2024-09-23T16:53:29Z |
| format | Article |
| id | mit-1721.1/97743 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:53:29Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/977432022-09-29T22:12:04Z Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States Moradi, Heidar Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang We propose a way—universal wave-function overlap—to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M[superscript d]) of closed spatial manifold M[superscript d]. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations. National Science Foundation (U.S.) (Grant DMR-1005541) National Natural Science Foundation (China) (Grant 11074140) National Natural Science Foundation (China) (Grant 11274192) Templeton Foundation 2015-07-15T13:28:17Z 2015-07-15T13:28:17Z 2015-07 2015-03 2015-07-14T22:00:20Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/97743 Moradi, Heidar, and Xiao-Gang Wen. "Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States." Phys. Rev. Lett. 115, 036802 (July 2015). Copyright © 2015 American Physical Society https://orcid.org/0000-0002-5874-581X en http://dx.doi.org/10.1103/PhysRevLett.115.036802 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Moradi, Heidar Wen, Xiao-Gang Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States |
| title | Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States |
| title_full | Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States |
| title_fullStr | Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States |
| title_full_unstemmed | Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States |
| title_short | Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States |
| title_sort | universal wave function overlap and universal topological data from generic gapped ground states |
| url | http://hdl.handle.net/1721.1/97743 https://orcid.org/0000-0002-5874-581X |
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