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@ARTICLE{Ferrando:639298,
      author       = {Ferrando, Gwenaël and Lamers, Jules and Levkovich-Maslyuk,
                      Fedor and Serban, Didina},
      title        = {{B}ethe {A}nsatz inside {C}alogero-{S}utherland models},
      journal      = {SciPost physics},
      volume       = {18},
      number       = {1},
      issn         = {2542-4653},
      address      = {Amsterdam},
      publisher    = {SciPost Foundation},
      reportid     = {PUBDB-2025-04399, arXiv:2308.16865. DESY-24-142},
      pages        = {035},
      year         = {2025},
      note         = {SciPost Phys. 18, 035 (2025). v1: 42 pages, 3 figures. v2:
                      minor improvements, 44 pages, 4 figures. v3: minor
                      improvements, published version, 44 pages, 4 figures},
      abstract     = {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.},
      keywords     = {spin: chain (INSPIRE) / symmetry: Yangian (INSPIRE) /
                      charge: conservation law (INSPIRE) / Bethe ansatz (INSPIRE)
                      / integrability (INSPIRE) / algebra (INSPIRE) / transfer
                      matrix (INSPIRE) / twist (INSPIRE) / fusion (INSPIRE) /
                      Calogero-Sutherland model (INSPIRE)},
      cin          = {T},
      ddc          = {530},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) /
                      BrokenSymmetries - Exact Results from Broken Symmetries
                      (101044226)},
      pid          = {G:(DE-HGF)POF4-611 / G:(EU-Grant)101044226},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2308.16865},
      howpublished = {arXiv:2308.16865},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2308.16865;\%\%$},
      doi          = {10.21468/SciPostPhys.18.1.035},
      url          = {https://bib-pubdb1.desy.de/record/639298},
}