Bethe ansatz inside Calogero-Sutherland models
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916662422274048 |
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| author | Ferrando, Gwenaël Lamers, Jules Levkovich-Maslyuk, Fedor Serban, Didina |
| author_facet | Ferrando, Gwenaël Lamers, Jules Levkovich-Maslyuk, Fedor Serban, Didina |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16865 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bethe ansatz inside Calogero-Sutherland models Ferrando, Gwenaël Lamers, Jules Levkovich-Maslyuk, Fedor Serban, Didina Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems 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. |
| title | Bethe ansatz inside Calogero-Sutherland models |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2308.16865 |