报告题目：Yangian descendants of the Haldane-Shastry spin chain

报告人：苗原  博士后（东京大学 Kavli IPMU）

报告时间：2026 年 6 月 12 日（周五）10 : 00-11 : 30

报告地点：北洋园校区 49 教 410 室

报告摘要：

        The Haldane-Shastry (HS) model is an exactly solvable spin chain with long-range interaction. A feature of the HS model is that the HS model possesses the Yangian symmetry on the lattice, while the spectrum has nice representation theory/combinatorics origin. The spectrum as well as the Yangian highest-weight states are known in the literature. However, the wavefunctions of the Yangian descendants are not obtained systematically as the highest-weight ones. I will explain how to construct the Yangian descendant states (by diagonalising a twisted transfer matrix) using algebraic Bethe ansatz (ABA), analogous to an inhomogeneous XXX spin chain. One special case recovers the renowned Gelfand-Tsetlin basis of Yangian. The Yangian descendants are labelled by quantum numbers that satisfy a set of effective Bethe equations, distinct from the highest-weight states that are labelled by motifs. Knowing the ABA, we are able to find the norms and overlaps between the Yangian descendant states. This allows us to obtain an orthonormal basis of the HS model, leading to possible physical applications.

报告人简介：

        Yuan Miao is a postdoctoral fellow at Kavli IPMU, University of Tokyo. His research interests are exactly solvable models, quantum integrability and other applications to mathematical physics.