Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems
Recent numerical work by Bardarson, Pollmann, and Moore revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interacti...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/80332 |
| _version_ | 1826193347477241856 |
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| author | Serbyn, Maksym Abanin, Dmitry A. Papic, Z. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Serbyn, Maksym Abanin, Dmitry A. Papic, Z. |
| author_sort | Serbyn, Maksym |
| collection | MIT |
| description | Recent numerical work by Bardarson, Pollmann, and Moore revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states. For weak interactions, we find that the entanglement entropy grows as ξln(Vt/ℏ), where V is the interaction strength, and ξ is the single-particle localization length. The saturated value of the entanglement entropy at long times is determined by the participation ratios of the initial state over the eigenstates of the subsystem. Our work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase. |
| first_indexed | 2024-09-23T09:37:35Z |
| format | Article |
| id | mit-1721.1/80332 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:37:35Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/803322022-09-30T15:45:54Z Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems Serbyn, Maksym Abanin, Dmitry A. Papic, Z. Massachusetts Institute of Technology. Department of Physics Serbyn, Maksym Recent numerical work by Bardarson, Pollmann, and Moore revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states. For weak interactions, we find that the entanglement entropy grows as ξln(Vt/ℏ), where V is the interaction strength, and ξ is the single-particle localization length. The saturated value of the entanglement entropy at long times is determined by the participation ratios of the initial state over the eigenstates of the subsystem. Our work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase. 2013-08-30T15:58:31Z 2013-08-30T15:58:31Z 2013-06 2013-06 Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/80332 Serbyn, Maksym, Z. Papić, and Dmitry A. Abanin. “Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems.” Physical Review Letters 110, no. 26 (June 2013). © 2013 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevLett.110.260601 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. application/pdf American Physical Society APS |
| spellingShingle | Serbyn, Maksym Abanin, Dmitry A. Papic, Z. Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems |
| title | Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems |
| title_full | Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems |
| title_fullStr | Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems |
| title_full_unstemmed | Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems |
| title_short | Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems |
| title_sort | universal slow growth of entanglement in interacting strongly disordered systems |
| url | http://hdl.handle.net/1721.1/80332 |
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