000639298 001__ 639298 000639298 005__ 20251125210900.0 000639298 0247_ $$2doi$$a10.21468/SciPostPhys.18.1.035 000639298 0247_ $$2INSPIRETeX$$aFerrando:2023lrx 000639298 0247_ $$2inspire$$ainspire:2692434 000639298 0247_ $$2arXiv$$aarXiv:2308.16865 000639298 0247_ $$2datacite_doi$$a10.3204/PUBDB-2025-04399 000639298 037__ $$aPUBDB-2025-04399 000639298 041__ $$aEnglish 000639298 082__ $$a530 000639298 088__ $$2arXiv$$aarXiv:2308.16865 000639298 088__ $$2DESY$$aDESY-24-142 000639298 1001_ $$aFerrando, Gwenaël$$b0 000639298 245__ $$aBethe Ansatz inside Calogero-Sutherland models 000639298 260__ $$aAmsterdam$$bSciPost Foundation$$c2025 000639298 3367_ $$2DRIVER$$aarticle 000639298 3367_ $$2DataCite$$aOutput Types/Journal article 000639298 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1764080566_3547559 000639298 3367_ $$2BibTeX$$aARTICLE 000639298 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000639298 3367_ $$00$$2EndNote$$aJournal Article 000639298 500__ $$aSciPost Phys. 18, 035 (2025). v1: 42 pages, 3 figures. v2: minor improvements, 44 pages, 4 figures. v3: minor improvements, published version, 44 pages, 4 figures 000639298 520__ $$aWe 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. 000639298 536__ $$0G:(DE-HGF)POF4-611$$a611 - Fundamental Particles and Forces (POF4-611)$$cPOF4-611$$fPOF IV$$x0 000639298 536__ $$0G:(EU-Grant)101044226$$aBrokenSymmetries - Exact Results from Broken Symmetries (101044226)$$c101044226$$fERC-2021-COG$$x1 000639298 588__ $$aDataset connected to CrossRef, INSPIRE, Journals: bib-pubdb1.desy.de 000639298 650_7 $$2INSPIRE$$aspin: chain 000639298 650_7 $$2INSPIRE$$asymmetry: Yangian 000639298 650_7 $$2INSPIRE$$acharge: conservation law 000639298 650_7 $$2INSPIRE$$aBethe ansatz 000639298 650_7 $$2INSPIRE$$aintegrability 000639298 650_7 $$2INSPIRE$$aalgebra 000639298 650_7 $$2INSPIRE$$atransfer matrix 000639298 650_7 $$2INSPIRE$$atwist 000639298 650_7 $$2INSPIRE$$afusion 000639298 650_7 $$2INSPIRE$$aCalogero-Sutherland model 000639298 693__ $$0EXP:(DE-MLZ)NOSPEC-20140101$$5EXP:(DE-MLZ)NOSPEC-20140101$$eNo specific instrument$$x0 000639298 7001_ $$0P:(DE-H253)PIP1028527$$aLamers, Jules$$b1$$eCorresponding author$$udesy 000639298 7001_ $$aLevkovich-Maslyuk, Fedor$$b2 000639298 7001_ $$aSerban, Didina$$b3 000639298 773__ $$0PERI:(DE-600)2886659-9$$a10.21468/SciPostPhys.18.1.035$$gVol. 18, no. 1, p. 035$$n1$$p035$$tSciPost physics$$v18$$x2542-4653$$y2025 000639298 7870_ $$0PUBDB-2024-05936$$aFerrando, Gwenaël et.al.$$d2024$$iIsParent$$rarXiv:2308.16865 ; DESY-24-142$$tBethe ansatz inside Calogero-Sutherland models 000639298 8564_ $$uhttps://bib-pubdb1.desy.de/record/639298/files/SciPostPhys_18_1_035.pdf$$yOpenAccess 000639298 8564_ $$uhttps://bib-pubdb1.desy.de/record/639298/files/SciPostPhys_18_1_035.pdf?subformat=pdfa$$xpdfa$$yOpenAccess 000639298 909CO $$ooai:bib-pubdb1.desy.de:639298$$popenaire$$popen_access$$pdriver$$pVDB$$pec_fundedresources$$pdnbdelivery 000639298 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1028527$$aDeutsches Elektronen-Synchrotron$$b1$$kDESY 000639298 9131_ $$0G:(DE-HGF)POF4-611$$1G:(DE-HGF)POF4-610$$2G:(DE-HGF)POF4-600$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$aDE-HGF$$bForschungsbereich Materie$$lMatter and the Universe$$vFundamental Particles and Forces$$x0 000639298 9141_ $$y2025 000639298 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)0160$$2StatID$$aDBCoverage$$bEssential Science Indicators$$d2025-01-02 000639298 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0 000639298 915__ $$0StatID:(DE-HGF)0100$$2StatID$$aJCR$$bSCIPOST PHYS : 2022$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)9905$$2StatID$$aIF >= 5$$bSCIPOST PHYS : 2022$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)0501$$2StatID$$aDBCoverage$$bDOAJ Seal$$d2021-04-19T09:27:06Z 000639298 915__ $$0StatID:(DE-HGF)0500$$2StatID$$aDBCoverage$$bDOAJ$$d2021-04-19T09:27:06Z 000639298 915__ $$0StatID:(DE-HGF)0113$$2StatID$$aWoS$$bScience Citation Index Expanded$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000639298 915__ $$0StatID:(DE-HGF)0030$$2StatID$$aPeer Review$$bDOAJ : Open peer review$$d2021-04-19T09:27:06Z 000639298 915__ $$0StatID:(DE-HGF)1150$$2StatID$$aDBCoverage$$bCurrent Contents - Physical, Chemical and Earth Sciences$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2025-01-02 000639298 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2025-01-02 000639298 9201_ $$0I:(DE-H253)T-20120731$$kT$$lTheorie-Gruppe$$x0 000639298 980__ $$ajournal 000639298 980__ $$aVDB 000639298 980__ $$aUNRESTRICTED 000639298 980__ $$aI:(DE-H253)T-20120731 000639298 9801_ $$aFullTexts