Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit
We present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example of this process, we compute a subset of the spectrum of the eclectic spin cha...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-08-01
|
| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321322002115 |
| _version_ | 1818536770404352000 |
|---|---|
| author | Juan Miguel Nieto García Leander Wyss |
| author_facet | Juan Miguel Nieto García Leander Wyss |
| author_sort | Juan Miguel Nieto García |
| collection | DOAJ |
| description | We present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example of this process, we compute a subset of the spectrum of the eclectic spin chain by means of the Nested Coordinate Bethe Ansatz. This allows us to show that the Bethe Ansatz of the finitely twisted spin chain contains enough information to reconstruct the generalised eigenvectors of the eclectic spin chain. |
| first_indexed | 2024-12-11T18:42:13Z |
| format | Article |
| id | doaj.art-19d0e90aedd049b4a9a57e0bb2a3eabf |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-11T18:42:13Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-19d0e90aedd049b4a9a57e0bb2a3eabf2022-12-22T00:54:35ZengElsevierNuclear Physics B0550-32132022-08-01981115860Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limitJuan Miguel Nieto García0Leander Wyss1Corresponding authors.; Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UKCorresponding authors.; Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UKWe present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example of this process, we compute a subset of the spectrum of the eclectic spin chain by means of the Nested Coordinate Bethe Ansatz. This allows us to show that the Bethe Ansatz of the finitely twisted spin chain contains enough information to reconstruct the generalised eigenvectors of the eclectic spin chain.http://www.sciencedirect.com/science/article/pii/S0550321322002115 |
| spellingShingle | Juan Miguel Nieto García Leander Wyss Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit Nuclear Physics B |
| title | Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit |
| title_full | Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit |
| title_fullStr | Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit |
| title_full_unstemmed | Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit |
| title_short | Jordan blocks and the Bethe Ansatz I: The eclectic spin chain as a limit |
| title_sort | jordan blocks and the bethe ansatz i the eclectic spin chain as a limit |
| url | http://www.sciencedirect.com/science/article/pii/S0550321322002115 |
| work_keys_str_mv | AT juanmiguelnietogarcia jordanblocksandthebetheansatzitheeclecticspinchainasalimit AT leanderwyss jordanblocksandthebetheansatzitheeclecticspinchainasalimit |