Entanglement spectrum of a random partition: Connection with the localization transition
We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability p ∈ [0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue...
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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/1721.1/97439 https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0002-3790-5511 |
| _version_ | 1826210572145786880 |
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| author | Vijay, Sagar Fu, Liang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Vijay, Sagar Fu, Liang |
| author_sort | Vijay, Sagar |
| collection | MIT |
| description | We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability p ∈ [0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability p, the entanglement Hamiltonian H[subscript A] must go through a topological phase transition driven by the percolation of a random network of edge states. As an example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions. |
| first_indexed | 2024-09-23T14:51:46Z |
| format | Article |
| id | mit-1721.1/97439 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:51:46Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/974392022-09-29T11:02:48Z Entanglement spectrum of a random partition: Connection with the localization transition Vijay, Sagar Fu, Liang Massachusetts Institute of Technology. Department of Physics Vijay, Sagar Fu, Liang We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability p ∈ [0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability p, the entanglement Hamiltonian H[subscript A] must go through a topological phase transition driven by the percolation of a random network of edge states. As an example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions. United States. Dept. of Energy. Division of Materials Sciences and Engineering (Award DE-SC0010526) 2015-06-16T15:11:11Z 2015-06-16T15:11:11Z 2015-06 2015-04 2015-06-15T22:00:07Z Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/97439 Vijay, Sagar, and Liang Fu. “Entanglement Spectrum of a Random Partition: Connection with the Localization Transition.” Phys. Rev. B 91, no. 22 (June 2015). © 2015 American Physical Society https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0002-3790-5511 en http://dx.doi.org/10.1103/PhysRevB.91.220101 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 | Vijay, Sagar Fu, Liang Entanglement spectrum of a random partition: Connection with the localization transition |
| title | Entanglement spectrum of a random partition: Connection with the localization transition |
| title_full | Entanglement spectrum of a random partition: Connection with the localization transition |
| title_fullStr | Entanglement spectrum of a random partition: Connection with the localization transition |
| title_full_unstemmed | Entanglement spectrum of a random partition: Connection with the localization transition |
| title_short | Entanglement spectrum of a random partition: Connection with the localization transition |
| title_sort | entanglement spectrum of a random partition connection with the localization transition |
| url | http://hdl.handle.net/1721.1/97439 https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0002-3790-5511 |
| work_keys_str_mv | AT vijaysagar entanglementspectrumofarandompartitionconnectionwiththelocalizationtransition AT fuliang entanglementspectrumofarandompartitionconnectionwiththelocalizationtransition |