Geometric proof of the equality between entanglement and edge spectra
The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal state of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics....
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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/1721.1/74251 https://orcid.org/0000-0003-4203-4148 |
| _version_ | 1826217255936983040 |
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| author | Swingle, Brian Gordon Todadri, Senthil |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Swingle, Brian Gordon Todadri, Senthil |
| author_sort | Swingle, Brian Gordon |
| collection | MIT |
| description | The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal state of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics. We give a simple geometric proof of the bulk-edge correspondence for a wide variety of physical systems. Our unified proof relies on geometric techniques available in Lorentz invariant and conformally invariant quantum field theories. These methods were originally developed in part to understand the physics of black holes, and we now apply them to determine the local structure of entanglement in quantum many-body systems. |
| first_indexed | 2024-09-23T17:00:29Z |
| format | Article |
| id | mit-1721.1/74251 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:00:29Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/742512022-09-29T23:03:12Z Geometric proof of the equality between entanglement and edge spectra Swingle, Brian Gordon Todadri, Senthil Massachusetts Institute of Technology. Department of Physics Swingle, Brian Gordon Todadri, Senthil The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal state of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics. We give a simple geometric proof of the bulk-edge correspondence for a wide variety of physical systems. Our unified proof relies on geometric techniques available in Lorentz invariant and conformally invariant quantum field theories. These methods were originally developed in part to understand the physics of black holes, and we now apply them to determine the local structure of entanglement in quantum many-body systems. Simons Foundation. Fellowship National Science Foundation (U.S.) (Grant DMR-1005434) 2012-10-25T17:32:11Z 2012-10-25T17:32:11Z 2012-07 2012-06 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/74251 Swingle, Brian, and T. Senthil. “Geometric Proof of the Equality Between Entanglement and Edge Spectra.” Physical Review B 86.4 (2012). ©2012 American Physical Society https://orcid.org/0000-0003-4203-4148 en_US http://dx.doi.org/10.1103/PhysRevB.86.045117 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 | Swingle, Brian Gordon Todadri, Senthil Geometric proof of the equality between entanglement and edge spectra |
| title | Geometric proof of the equality between entanglement and edge spectra |
| title_full | Geometric proof of the equality between entanglement and edge spectra |
| title_fullStr | Geometric proof of the equality between entanglement and edge spectra |
| title_full_unstemmed | Geometric proof of the equality between entanglement and edge spectra |
| title_short | Geometric proof of the equality between entanglement and edge spectra |
| title_sort | geometric proof of the equality between entanglement and edge spectra |
| url | http://hdl.handle.net/1721.1/74251 https://orcid.org/0000-0003-4203-4148 |
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