Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry
We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical difficulties due to the breaking of (1) symmetry an...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2023 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211985 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry. Dmitry Chernyak, Azat M. Gainutdinov, Jesper Lykke Jacobsen and Hubert Saleur. SIGMA 19 (2023), 046, 47 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741154240397312 |
|---|---|
| author | Chernyak, Dmitry Gainutdinov, Azat M. Jacobsen, Jesper Lykke Saleur, Hubert |
| author_facet | Chernyak, Dmitry Gainutdinov, Azat M. Jacobsen, Jesper Lykke Saleur, Hubert |
| citation_txt | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry. Dmitry Chernyak, Azat M. Gainutdinov, Jesper Lykke Jacobsen and Hubert Saleur. SIGMA 19 (2023), 046, 47 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical difficulties due to the breaking of (1) symmetry and the absence of a reference state are overcome by an algebraic construction where the two-boundary Temperley-Lieb Hamiltonian is realised in a new ₂-invariant spin chain involving infinite-dimensional Verma modules on the edges [J. High Energy Phys. 2022 (2022), no. 11, 016, 64 pages, arXiv:2207.12772]. The equivalence of the two Hamiltonians is established by proving Schur-Weyl duality between ₂ and the two-boundary Temperley-Lieb algebra. In this framework, the Nepomechie condition turns out to have a simple algebraic interpretation in terms of quantum group fusion rules.
|
| first_indexed | 2026-04-17T17:53:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211985 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T17:53:16Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chernyak, Dmitry Gainutdinov, Azat M. Jacobsen, Jesper Lykke Saleur, Hubert 2026-01-20T16:14:30Z 2023 Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry. Dmitry Chernyak, Azat M. Gainutdinov, Jesper Lykke Jacobsen and Hubert Saleur. SIGMA 19 (2023), 046, 47 pages 1815-0659 2020 Mathematics Subject Classification: 81R50; 81R12; 81U15; 16T25 arXiv:2212.09696 https://nasplib.isofts.kiev.ua/handle/123456789/211985 https://doi.org/10.3842/SIGMA.2023.046 We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical difficulties due to the breaking of (1) symmetry and the absence of a reference state are overcome by an algebraic construction where the two-boundary Temperley-Lieb Hamiltonian is realised in a new ₂-invariant spin chain involving infinite-dimensional Verma modules on the edges [J. High Energy Phys. 2022 (2022), no. 11, 016, 64 pages, arXiv:2207.12772]. The equivalence of the two Hamiltonians is established by proving Schur-Weyl duality between ₂ and the two-boundary Temperley-Lieb algebra. In this framework, the Nepomechie condition turns out to have a simple algebraic interpretation in terms of quantum group fusion rules. We are thankful to Samuel Belliard, Rouven Frassek, and Karol Kozlowski for useful discussions. We thank the anonymous referees for their constructive comments. This work was supported by the French Agence Nationale de la Recherche (ANR) under grant ANR-21-CE40-0003 (project CONFICA). The work of A.M.G. was supported by the CNRS, and partially by the ANR grant JCJC ANR-18-CE40-0001 and the RSF Grant No. 20-61-46005. A.M.G. is also grateful to IPHT Saclay and LPENS in Paris for their kind hospitality during the visits in 2022. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry Article published earlier |
| spellingShingle | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry Chernyak, Dmitry Gainutdinov, Azat M. Jacobsen, Jesper Lykke Saleur, Hubert |
| title | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry |
| title_full | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry |
| title_fullStr | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry |
| title_full_unstemmed | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry |
| title_short | Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via ₂ Symmetry |
| title_sort | algebraic bethe ansatz for the open xxz spin chain with non-diagonal boundary terms via ₂ symmetry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211985 |
| work_keys_str_mv | AT chernyakdmitry algebraicbetheansatzfortheopenxxzspinchainwithnondiagonalboundarytermsvia2symmetry AT gainutdinovazatm algebraicbetheansatzfortheopenxxzspinchainwithnondiagonalboundarytermsvia2symmetry AT jacobsenjesperlykke algebraicbetheansatzfortheopenxxzspinchainwithnondiagonalboundarytermsvia2symmetry AT saleurhubert algebraicbetheansatzfortheopenxxzspinchainwithnondiagonalboundarytermsvia2symmetry |