Journal Article

PUBDB-2025-04399

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Bethe Ansatz inside Calogero-Sutherland models

Ferrando, G. ; Lamers, J. (Corresponding author)DESY* ; Levkovich-Maslyuk, F. ; Serban, D.

2025
SciPost Foundation Amsterdam

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Please use a persistent id in citations: doi:10.21468/SciPostPhys.18.1.035  doi:10.3204/PUBDB-2025-04399

Report No.: DESY-24-142; arXiv:2308.16865

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.

Keyword(s): spin: chain ; symmetry: Yangian ; charge: conservation law ; Bethe ansatz ; integrability ; algebra ; transfer matrix ; twist ; fusion ; Calogero-Sutherland model

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

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. BrokenSymmetries - Exact Results from Broken Symmetries (101044226) (101044226)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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Database coverage:
; ; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; DOAJ Seal ; Essential Science Indicators ; IF >= 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Ferrando, G. ; Lamers, J. (Corresponding author)DESY* ; Levkovich-Maslyuk, F. ; Serban, D.
Bethe ansatz inside Calogero-Sutherland models
[10.3204/PUBDB-2024-05936]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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