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arXiv · 0706.0688

Bethe Algebra of Homogeneous XXX Heisenberg Model Has Simple Spectrum

E. Mukhin·V. Tarasov·A. Varchenko
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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 $°f = l, °g = n-l+1$ and $f(u)g(u-1) - f(u-1)g(u) = (u+1)^n$.

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BibTeXRIS

E. Mukhin, V. Tarasov, A. Varchenko. 2012-05-25. Bethe Algebra of Homogeneous XXX Heisenberg Model Has Simple Spectrum. https://arxiv.org/abs/0706.0688

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