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Article Dans Une Revue J.Phys.A Année : 2024

From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry spin chain by freezing

Résumé

The Haldane-Shastry spin chain is a long-range model known to enjoy a myriad of remarkable properties, including Yangian symmetry and, for spin 1/2, explicit highest-weight eigenvectors featuring Jack polynomials, or more precisely its zonal spherical special case. These properties stem from the spin-Calogero-Sutherland model, which reduces to Haldane-Shastry in a special 'freezing' limit. In this work we clarify some points that, to the best of our knowledge, were missing in the literature. We have two main results. First, we show that freezing the fermionic spin-Calogero-Sutherland naturally accounts for the form of the explicit Haldane-Shastry wave functions. Second, we give a proof of the claim of Bernard, Gaudin, Haldane and Pasquier that the Yangian highest-weight eigenvectors of the $\mathfrak{sl}_r$ version of the Haldane-Shastry spin chain arise from freezing $\mathfrak{sl}_{r-1}$ spin-Calogero-Sutherland eigenvectors at the zonal spherical point $\alpha^\star = 1/2$.

Dates et versions

hal-03908165 , version 1 (20-12-2022)

Identifiants

Citer

Jules Lamers, Didina Serban. From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry spin chain by freezing. J.Phys.A, 2024, ⟨10.1088/1751-8121/ad4b79⟩. ⟨hal-03908165⟩
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