Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling
Abstract Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2017)136 |
| _version_ | 1819212852759625728 |
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| author | Pramod Padmanabhan Soo-Jong Rey Daniel Teixeira Diego Trancanelli |
| author_facet | Pramod Padmanabhan Soo-Jong Rey Daniel Teixeira Diego Trancanelli |
| author_sort | Pramod Padmanabhan |
| collection | DOAJ |
| description | Abstract Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries. |
| first_indexed | 2024-12-23T06:49:33Z |
| format | Article |
| id | doaj.art-a0956060ff784474b7730ac2b3e4e64e |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T06:49:33Z |
| publishDate | 2017-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a0956060ff784474b7730ac2b3e4e64e2022-12-21T17:56:29ZengSpringerOpenJournal of High Energy Physics1029-84792017-05-012017514010.1007/JHEP05(2017)136Supersymmetric many-body systems from partial symmetries — integrability, localization and scramblingPramod Padmanabhan0Soo-Jong Rey1Daniel Teixeira2Diego Trancanelli3Fields, Gravity & Strings, CTPU, Institute for Basic ScienceFields, Gravity & Strings, CTPU, Institute for Basic ScienceInstitute of Physics, University of São PauloInstitute of Physics, University of São PauloAbstract Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.http://link.springer.com/article/10.1007/JHEP05(2017)136Discrete SymmetriesExtended SupersymmetryLattice Integrable ModelsRandom Systems |
| spellingShingle | Pramod Padmanabhan Soo-Jong Rey Daniel Teixeira Diego Trancanelli Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling Journal of High Energy Physics Discrete Symmetries Extended Supersymmetry Lattice Integrable Models Random Systems |
| title | Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling |
| title_full | Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling |
| title_fullStr | Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling |
| title_full_unstemmed | Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling |
| title_short | Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling |
| title_sort | supersymmetric many body systems from partial symmetries integrability localization and scrambling |
| topic | Discrete Symmetries Extended Supersymmetry Lattice Integrable Models Random Systems |
| url | http://link.springer.com/article/10.1007/JHEP05(2017)136 |
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