Constructs Yangian descendants for the Haldane-Shastry chain via algebraic Bethe ansatz and derives norms and overlaps formulae.
Bethe Algebra of Homogeneous XXX Heisenberg Model Has Simple Spectrum
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abstract
We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional $gl_2$-modules. As a byproduct we show that there exist exactly $\binom {n}{l}-\binom{n}{l-1}$ two-dimensional vector subspaces $V \subset \C[u]$ with a basis $f,g\in V$ such that $\deg f = l, \deg g = n-l+1$ and $f(u)g(u-1) - f(u-1)g(u) = (u+1)^n$.
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cond-mat.stat-mech 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Norms, overlaps and Yangian descendants for the Haldane--Shastry spin chain
Constructs Yangian descendants for the Haldane-Shastry chain via algebraic Bethe ansatz and derives norms and overlaps formulae.