Bethe Ansatz inside Calogero-Sutherland models
We study the trigonometric quantum spin-Calogero–Sutherland model, and the Haldane–Shastry spin chain as a special case, using a Bethe-Ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability for Heisenberg spin chains into the world of integrable l...
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| Language: | English |
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2025-01-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.1.035 |
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| author | Gwenaël Ferrando, Jules Lamers, Fedor Levkovich-Maslyuk, Didina Serban |
| author_facet | Gwenaël Ferrando, Jules Lamers, Fedor Levkovich-Maslyuk, Didina Serban |
| author_sort | Gwenaël Ferrando, Jules Lamers, Fedor Levkovich-Maslyuk, Didina Serban |
| collection | DOAJ |
| description | We study the trigonometric quantum spin-Calogero–Sutherland model, and the Haldane–Shastry spin chain as a special case, using a Bethe-Ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability for Heisenberg spin chains into the world of integrable long-range models with spins. From the transfer matrix with a diagonal twist we construct Heisenberg-style symmetries (Bethe algebra) that refine the usual hierarchy of commuting Hamiltonians (quantum determinant) of the spin-Calogero–Sutherland model. We compute the first few of these new conserved charges explicitly, and diagonalise them by Bethe Ansatz inside each irreducible Yangian representation. This yields a new eigenbasis for the spin-Calogero–Sutherland model that generalises the Yangian Gelfand–Tsetlin basis of Takemura–Uglov. The Bethe-Ansatz analysis involves non-generic values of the inhomogeneities. Our review of the inhomogeneous Heisenberg XXX chain, with special attention to how the Bethe Ansatz works in the presence of fusion, may be of independent interest. |
| format | Article |
| id | doaj-art-b148b2812de14dd1b1d45d51e7dcf14a |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-b148b2812de14dd1b1d45d51e7dcf14a2025-01-28T16:02:55ZengSciPostSciPost Physics2542-46532025-01-0118103510.21468/SciPostPhys.18.1.035Bethe Ansatz inside Calogero-Sutherland modelsGwenaël Ferrando, Jules Lamers, Fedor Levkovich-Maslyuk, Didina SerbanWe study the trigonometric quantum spin-Calogero–Sutherland model, and the Haldane–Shastry spin chain as a special case, using a Bethe-Ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability for Heisenberg spin chains into the world of integrable long-range models with spins. From the transfer matrix with a diagonal twist we construct Heisenberg-style symmetries (Bethe algebra) that refine the usual hierarchy of commuting Hamiltonians (quantum determinant) of the spin-Calogero–Sutherland model. We compute the first few of these new conserved charges explicitly, and diagonalise them by Bethe Ansatz inside each irreducible Yangian representation. This yields a new eigenbasis for the spin-Calogero–Sutherland model that generalises the Yangian Gelfand–Tsetlin basis of Takemura–Uglov. The Bethe-Ansatz analysis involves non-generic values of the inhomogeneities. Our review of the inhomogeneous Heisenberg XXX chain, with special attention to how the Bethe Ansatz works in the presence of fusion, may be of independent interest.https://scipost.org/SciPostPhys.18.1.035 |
| spellingShingle | Gwenaël Ferrando, Jules Lamers, Fedor Levkovich-Maslyuk, Didina Serban Bethe Ansatz inside Calogero-Sutherland models SciPost Physics |
| title | Bethe Ansatz inside Calogero-Sutherland models |
| title_full | Bethe Ansatz inside Calogero-Sutherland models |
| title_fullStr | Bethe Ansatz inside Calogero-Sutherland models |
| title_full_unstemmed | Bethe Ansatz inside Calogero-Sutherland models |
| title_short | Bethe Ansatz inside Calogero-Sutherland models |
| title_sort | bethe ansatz inside calogero sutherland models |
| url | https://scipost.org/SciPostPhys.18.1.035 |
| work_keys_str_mv | AT gwenaelferrandojuleslamersfedorlevkovichmaslyukdidinaserban betheansatzinsidecalogerosutherlandmodels |