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arXiv · 2606.20168

Norms, overlaps and Yangian descendants for the Haldane-Shastry spin chain

Yunfeng Jiang·Jules Lamers·Yuan Miao
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Abstract

The Haldane-Shastry spin chain is a prototypical integrable model with long-range interactions, notable for hosting quasiparticles with fractional statistics and serving as a discrete analogue of a conformal field theory. Its remarkable simplicity is closely tied to a full Yangian spin symmetry. While the highest-weight states for this symmetry are known explicitly, a systematic treatment of the descendant states, needed for the computation of various physical quantities, has remained incomplete. In this work, we provide a detailed construction of these descendants in terms of the algebraic Bethe ansatz following recent work of Ferrando et al. In the limit of extreme twist, it includes the Gelfand-Tsetlin basis. As an application, we derive product and determinant formulae for norms and overlaps of these states.

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Yunfeng Jiang, Jules Lamers, Yuan Miao. 2026-06-18. Norms, overlaps and Yangian descendants for the Haldane-Shastry spin chain. https://arxiv.org/abs/2606.20168

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