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000639298 1001_ $$aFerrando, Gwenaël$$b0
000639298 245__ $$aBethe Ansatz inside Calogero-Sutherland models
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000639298 500__ $$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__ $$aWe study the trigonometric quantum spin-Calogero–Sutherland model, and the Haldane–Shastry spin chain as a special case, using a Bethe-Ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability for Heisenberg spin chains into the world of integrable long-range models with spins. From the transfer matrix with a diagonal twist we construct Heisenberg-style symmetries (Bethe algebra) that refine the usual hierarchy of commuting Hamiltonians (quantum determinant) of the spin-Calogero–Sutherland model. We compute the first few of these new conserved charges explicitly, and diagonalise them by Bethe Ansatz inside each irreducible Yangian representation. This yields a new eigenbasis for the spin-Calogero–Sutherland model that generalises the Yangian Gelfand–Tsetlin basis of Takemura–Uglov. The Bethe-Ansatz analysis involves non-generic values of the inhomogeneities. Our review of the inhomogeneous Heisenberg XXX chain, with special attention to how the Bethe Ansatz works in the presence of fusion, may be of independent interest.
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000639298 536__ $$0G:(EU-Grant)101044226$$aBrokenSymmetries - Exact Results from Broken Symmetries (101044226)$$c101044226$$fERC-2021-COG$$x1
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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
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000639298 650_7 $$2INSPIRE$$aCalogero-Sutherland model
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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
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