A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations
We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of fermion topological quantum order, building on a model presented by S. Vijay, T. H. Hsieh, and L. Fu [Phys. Rev. X 5, 041038 (2015)10.1103/PhysRevX.5.041038]. These models hav...
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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/1721.1/100514 https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0002-3790-5511 https://orcid.org/0000-0002-4420-4932 |
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| author | Haah, Jeongwan Fu, Liang Vijay, Ksheerasagar |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Haah, Jeongwan Fu, Liang Vijay, Ksheerasagar |
| author_sort | Haah, Jeongwan |
| collection | MIT |
| description | We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of fermion topological quantum order, building on a model presented by S. Vijay, T. H. Hsieh, and L. Fu [Phys. Rev. X 5, 041038 (2015)10.1103/PhysRevX.5.041038]. These models have extensive topological ground-state degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the lattice. In particular, one of our models has fundamental excitations that are completely stationary. To demonstrate these results, we introduce a powerful polynomial representation of commuting Majorana Hamiltonians. Remarkably, the physical properties of the topologically ordered state are encoded in an algebraic variety, defined by the common zeros of a set of polynomials over a finite field. This provides a “geometric” framework for the emergence of topological order. |
| first_indexed | 2024-09-23T13:45:28Z |
| format | Article |
| id | mit-1721.1/100514 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:45:28Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1005142022-09-28T15:59:01Z A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations Haah, Jeongwan Fu, Liang Vijay, Ksheerasagar Massachusetts Institute of Technology. Department of Physics Vijay, Ksheerasagar Haah, Jeongwan Fu, Liang We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of fermion topological quantum order, building on a model presented by S. Vijay, T. H. Hsieh, and L. Fu [Phys. Rev. X 5, 041038 (2015)10.1103/PhysRevX.5.041038]. These models have extensive topological ground-state degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the lattice. In particular, one of our models has fundamental excitations that are completely stationary. To demonstrate these results, we introduce a powerful polynomial representation of commuting Majorana Hamiltonians. Remarkably, the physical properties of the topologically ordered state are encoded in an algebraic variety, defined by the common zeros of a set of polynomials over a finite field. This provides a “geometric” framework for the emergence of topological order. David & Lucile Packard Foundation United States. Dept. of Energy. Division of Materials Sciences and Engineering (Award DE-SC0010526) MIT Department of Physics Pappalardo Program 2015-12-27T23:51:05Z 2015-12-27T23:51:05Z 2015-12 2015-11 2015-12-21T23:00:07Z Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/100514 Vijay, Sagar, Jeongwan Haah, and Liang Fu. “A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations.” Physical Review B 92, no. 23 (December 21, 2015). © 2015 American Physical Society https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0002-3790-5511 https://orcid.org/0000-0002-4420-4932 en http://dx.doi.org/10.1103/PhysRevB.92.235136 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 | Haah, Jeongwan Fu, Liang Vijay, Ksheerasagar A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations |
| title | A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations |
| title_full | A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations |
| title_fullStr | A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations |
| title_full_unstemmed | A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations |
| title_short | A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations |
| title_sort | new kind of topological quantum order a dimensional hierarchy of quasiparticles built from stationary excitations |
| url | http://hdl.handle.net/1721.1/100514 https://orcid.org/0000-0002-8803-1017 https://orcid.org/0000-0002-3790-5511 https://orcid.org/0000-0002-4420-4932 |
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