Topological defects in Floquet circuits
We introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes wi...
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2024-03-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.16.3.075 |
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| _version_ | 1825206259697057792 |
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| author | Mao Tian Tan, Yifan Wang, Aditi Mitra |
| author_facet | Mao Tian Tan, Yifan Wang, Aditi Mitra |
| author_sort | Mao Tian Tan, Yifan Wang, Aditi Mitra |
| collection | DOAJ |
| description | We introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes with such defects, but the duality defect is not unitary, as it projects out half the states. We give two applications of these defects. One is to analyze the return amplitudes in the presence of "space-like" defects stretching around the system. We verify explicitly that the return amplitudes are in agreement with the fusion rules of the defects. The second application is to study unitary evolution in the presence of "time-like" defects that implement anti-periodic and duality-twisted boundary conditions. We show that a single unpaired localized Majorana zero mode appears in the latter case. We explicitly construct this operator, which acts as a symmetry of this Floquet circuit. We also present analytic expressions for the entanglement entropy after a single time step for a system of a few sites, for all of the above defect configurations. |
| format | Article |
| id | doaj-art-b1b5c46094cf40a8a9ffa2deb81347d4 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-b1b5c46094cf40a8a9ffa2deb81347d42025-02-07T11:17:27ZengSciPostSciPost Physics2542-46532024-03-0116307510.21468/SciPostPhys.16.3.075Topological defects in Floquet circuitsMao Tian Tan, Yifan Wang, Aditi MitraWe introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes with such defects, but the duality defect is not unitary, as it projects out half the states. We give two applications of these defects. One is to analyze the return amplitudes in the presence of "space-like" defects stretching around the system. We verify explicitly that the return amplitudes are in agreement with the fusion rules of the defects. The second application is to study unitary evolution in the presence of "time-like" defects that implement anti-periodic and duality-twisted boundary conditions. We show that a single unpaired localized Majorana zero mode appears in the latter case. We explicitly construct this operator, which acts as a symmetry of this Floquet circuit. We also present analytic expressions for the entanglement entropy after a single time step for a system of a few sites, for all of the above defect configurations.https://scipost.org/SciPostPhys.16.3.075 |
| spellingShingle | Mao Tian Tan, Yifan Wang, Aditi Mitra Topological defects in Floquet circuits SciPost Physics |
| title | Topological defects in Floquet circuits |
| title_full | Topological defects in Floquet circuits |
| title_fullStr | Topological defects in Floquet circuits |
| title_full_unstemmed | Topological defects in Floquet circuits |
| title_short | Topological defects in Floquet circuits |
| title_sort | topological defects in floquet circuits |
| url | https://scipost.org/SciPostPhys.16.3.075 |
| work_keys_str_mv | AT maotiantanyifanwangaditimitra topologicaldefectsinfloquetcircuits |