Tensor-product representations for string-net condensed states
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPSs). These TPSs are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry-breaking states) and states with long-range entanglement...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/51745 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826192670780817408 |
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| author | Gu, Zheng-Cheng Levin, Michael Swingle, Brian Gordon Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Gu, Zheng-Cheng Levin, Michael Swingle, Brian Gordon Wen, Xiao-Gang |
| author_sort | Gu, Zheng-Cheng |
| collection | MIT |
| description | We show that general string-net condensed states have a natural representation in terms of tensor product states (TPSs). These TPSs are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry-breaking states) and states with long-range entanglement (such as string-net condensed states with topological/quantum order). The tensor product representation provides a kind of “mean-field” description for topologically ordered states and could be a powerful way to study quantum phase transitions between such states. As an attempt in this direction, we show that the constructed TPSs are fixed points under a certain wave-function renormalization-group transformation for quantum states. |
| first_indexed | 2024-09-23T09:27:29Z |
| format | Article |
| id | mit-1721.1/51745 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:27:29Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/517452022-09-26T11:30:45Z Tensor-product representations for string-net condensed states Gu, Zheng-Cheng Levin, Michael Swingle, Brian Gordon Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Gu, Zheng-Cheng Swingle, Brian Gordon Wen, Xiao-Gang We show that general string-net condensed states have a natural representation in terms of tensor product states (TPSs). These TPSs are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry-breaking states) and states with long-range entanglement (such as string-net condensed states with topological/quantum order). The tensor product representation provides a kind of “mean-field” description for topologically ordered states and could be a powerful way to study quantum phase transitions between such states. As an attempt in this direction, we show that the constructed TPSs are fixed points under a certain wave-function renormalization-group transformation for quantum states. Foundational Questions Institute (FQXi) National Science Foundation 2010-02-12T15:40:10Z 2010-02-12T15:40:10Z 2009-02 2008-09 Article http://purl.org/eprint/type/JournalArticle 1550-235X 1098-0121 http://hdl.handle.net/1721.1/51745 Gu, Zheng-Cheng et al. “Tensor-product representations for string-net condensed states.” Physical Review B 79.8 (2009): 085118. © 2009 The American Physical Society. https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.79.085118 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 APS |
| spellingShingle | Gu, Zheng-Cheng Levin, Michael Swingle, Brian Gordon Wen, Xiao-Gang Tensor-product representations for string-net condensed states |
| title | Tensor-product representations for string-net condensed states |
| title_full | Tensor-product representations for string-net condensed states |
| title_fullStr | Tensor-product representations for string-net condensed states |
| title_full_unstemmed | Tensor-product representations for string-net condensed states |
| title_short | Tensor-product representations for string-net condensed states |
| title_sort | tensor product representations for string net condensed states |
| url | http://hdl.handle.net/1721.1/51745 https://orcid.org/0000-0002-5874-581X |
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