Tensor network implementation of bulk entanglement spectrum
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs, and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2014
|
| Online Access: | http://hdl.handle.net/1721.1/89194 https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0001-8187-7266 |
| _version_ | 1811098126933557248 |
|---|---|
| author | Fu, Liang Qi, Xiao-Liang Hsieh, Timothy Hwa-wei |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Fu, Liang Qi, Xiao-Liang Hsieh, Timothy Hwa-wei |
| author_sort | Fu, Liang |
| collection | MIT |
| description | Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs, and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing such topological phase transitions in terms of the boundary degrees of freedom which mediate it. To do so, we make use of a correspondence between a topologically nontrivial ground state and its phase transition to a trivial phase established in T. Hsieh and L. Fu (arXiv:1305.1949). This involved computing the bulk entanglement spectrum (BES) of the ground state upon tracing out an extensive subsystem. This work implements BES via tensor network representations of ground states. In this framework, the universality class of the quantum critical entanglement Hamiltonian in d spatial dimensions is either derived analytically or mapped to a classical statistical model in d + 1 dimensions, which can be studied using Monte Carlo or tensor renormalization-group methods. As an example, we analytically derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase and demonstrate that the Affleck-Kennedy-Lieb-Tasaki (AKLT) wave function (and its generalizations) remarkably contains critical six-vertex (and, in general, eight-vertex) models within it. |
| first_indexed | 2024-09-23T17:10:20Z |
| format | Article |
| id | mit-1721.1/89194 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:10:20Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/891942022-10-03T10:53:28Z Tensor network implementation of bulk entanglement spectrum Fu, Liang Qi, Xiao-Liang Hsieh, Timothy Hwa-wei Massachusetts Institute of Technology. Department of Physics Hsieh, Timothy Hwa-wei Fu, Liang Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs, and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing such topological phase transitions in terms of the boundary degrees of freedom which mediate it. To do so, we make use of a correspondence between a topologically nontrivial ground state and its phase transition to a trivial phase established in T. Hsieh and L. Fu (arXiv:1305.1949). This involved computing the bulk entanglement spectrum (BES) of the ground state upon tracing out an extensive subsystem. This work implements BES via tensor network representations of ground states. In this framework, the universality class of the quantum critical entanglement Hamiltonian in d spatial dimensions is either derived analytically or mapped to a classical statistical model in d + 1 dimensions, which can be studied using Monte Carlo or tensor renormalization-group methods. As an example, we analytically derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase and demonstrate that the Affleck-Kennedy-Lieb-Tasaki (AKLT) wave function (and its generalizations) remarkably contains critical six-vertex (and, in general, eight-vertex) models within it. National Science Foundation (U.S.). Graduate Research Fellowship (0645960) United States. Dept. of Energy. Division of Materials Sciences and Engineering (Award DE-SC0010526) 2014-09-05T13:35:58Z 2014-09-05T13:35:58Z 2014-08 2014-07 2014-08-28T18:49:19Z Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/89194 Hsieh, Timothy H., Liang Fu, and Xiao-Liang Qi. “Tensor Network Implementation of Bulk Entanglement Spectrum.” Phys. Rev. B 90, no. 8 (August 2014). © 2014 American Physical Society https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0001-8187-7266 en http://dx.doi.org/10.1103/PhysRevB.90.085137 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Fu, Liang Qi, Xiao-Liang Hsieh, Timothy Hwa-wei Tensor network implementation of bulk entanglement spectrum |
| title | Tensor network implementation of bulk entanglement spectrum |
| title_full | Tensor network implementation of bulk entanglement spectrum |
| title_fullStr | Tensor network implementation of bulk entanglement spectrum |
| title_full_unstemmed | Tensor network implementation of bulk entanglement spectrum |
| title_short | Tensor network implementation of bulk entanglement spectrum |
| title_sort | tensor network implementation of bulk entanglement spectrum |
| url | http://hdl.handle.net/1721.1/89194 https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0001-8187-7266 |
| work_keys_str_mv | AT fuliang tensornetworkimplementationofbulkentanglementspectrum AT qixiaoliang tensornetworkimplementationofbulkentanglementspectrum AT hsiehtimothyhwawei tensornetworkimplementationofbulkentanglementspectrum |