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Spin generalizations of the classical elliptic Calogero--Inozemtsev model and integrable models of interacting tops associated with the BCn root system

  • D. Domanevsky
  • A. Zotov
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Abstract

We construct Lax pairs with a spectral parameter for a family of models of interacting tops associated with the BCn root system. The construction uses the parametric BCn associative Yang--Baxter equations, which involve both quantum R-matrices and boundary K-matrices satisfying the reflection equation. Special cases yield spin generalizations of the elliptic Calogero--Inozemtsev model. We also show how quantum Hamiltonians of interacting tops, combined with the Polychronakos freezing prescription, reproduce recently introduced anisotropic quantum long-range spin chains of Haldane--Shastry--Inozemtsev type.

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Cite

BibTeXRIS
BibTeX
@misc{domanevsky2026spin,
  title = {{Spin generalizations of the classical elliptic Calogero--Inozemtsev model and integrable models of interacting tops associated with the $\rmBC_n$ root system}},
  author = {D. Domanevsky and A. Zotov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37165},
  eprint = {2610.37165},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37165},
}
RIS
TY  - UNPB
TI  - Spin generalizations of the classical elliptic Calogero--Inozemtsev model and integrable models of interacting tops associated with the BC_n root system
AU  - D. Domanevsky
AU  - A. Zotov
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37165
UR  - https://arxiv.org/abs/2610.37165
AB  - We construct Lax pairs with a spectral parameter for a family of models of interacting tops associated with the BC_n root system. The construction uses the parametric BC_n associative Yang--Baxter equations, which involve both quantum R-matrices and boundary K-matrices satisfying the reflection equation. Special cases yield spin generalizations of the elliptic Calogero--Inozemtsev model. We also show how quantum Hamiltonians of interacting tops, combined with the Polychronakos freezing prescription, reproduce recently introduced anisotropic quantum long-range spin chains of Haldane--Shastry--Inozemtsev type.
ER  -