Frustration-free Hamiltonians supporting Majorana zero edge modes
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical stud...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aa88da |
| _version_ | 1797750610393563136 |
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| author | Sania Jevtic Ryan Barnett |
| author_facet | Sania Jevtic Ryan Barnett |
| author_sort | Sania Jevtic |
| collection | DOAJ |
| description | A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. |
| first_indexed | 2024-03-12T16:35:20Z |
| format | Article |
| id | doaj.art-3b94f81efba84ac28407f757ef744efe |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:20Z |
| publishDate | 2017-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-3b94f81efba84ac28407f757ef744efe2023-08-08T14:53:36ZengIOP PublishingNew Journal of Physics1367-26302017-01-01191010303410.1088/1367-2630/aa88daFrustration-free Hamiltonians supporting Majorana zero edge modesSania Jevtic0Ryan Barnett1Department of Mathematics, Huxley Building, Imperial College, London SW7 2AZ, United KingdomDepartment of Mathematics, Huxley Building, Imperial College, London SW7 2AZ, United KingdomA one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.https://doi.org/10.1088/1367-2630/aa88daMajorana zero modesfrustration-free Hamiltonianstopological phasesgapped systemsone-dimensional systemsfermionic systems |
| spellingShingle | Sania Jevtic Ryan Barnett Frustration-free Hamiltonians supporting Majorana zero edge modes New Journal of Physics Majorana zero modes frustration-free Hamiltonians topological phases gapped systems one-dimensional systems fermionic systems |
| title | Frustration-free Hamiltonians supporting Majorana zero edge modes |
| title_full | Frustration-free Hamiltonians supporting Majorana zero edge modes |
| title_fullStr | Frustration-free Hamiltonians supporting Majorana zero edge modes |
| title_full_unstemmed | Frustration-free Hamiltonians supporting Majorana zero edge modes |
| title_short | Frustration-free Hamiltonians supporting Majorana zero edge modes |
| title_sort | frustration free hamiltonians supporting majorana zero edge modes |
| topic | Majorana zero modes frustration-free Hamiltonians topological phases gapped systems one-dimensional systems fermionic systems |
| url | https://doi.org/10.1088/1367-2630/aa88da |
| work_keys_str_mv | AT saniajevtic frustrationfreehamiltonianssupportingmajoranazeroedgemodes AT ryanbarnett frustrationfreehamiltonianssupportingmajoranazeroedgemodes |