论文标题
Heun Lie类型的操作员和修改的代数Bethe Ansatz
Heun operator of Lie type and the modified algebraic Bethe ansatz
论文作者
论文摘要
Lie类型的通用HEUN操作员被确定为磁场中的某个$ bc $ gaudin磁铁哈密顿量。通过使用引入的Gaudin模型对角线化的修改代数Bethe Ansatz，我们根据不均匀的Bethe方程的伯特（Bethe）根部获得了Lie类型的通用Heun操作员的光谱。我们还表明，这些伯特的根与差分HEUN方程的多项式溶液的根密切相关。我们说明了这种方法在两种情况下的使用：$ o（3）$的表示理论以及在Krawtchouk链上免费的费米子的纠缠熵计算。
The generic Heun operator of Lie type is identified as a certain $BC$-Gaudin magnet Hamiltonian in a magnetic field. By using the modified algebraic Bethe ansatz introduced to diagonalize such Gaudin models, we obtain the spectrum of the generic Heun operator of Lie type in terms of the Bethe roots of inhomogeneous Bethe equations. We show also that these Bethe roots are intimately associated to the roots of polynomial solutions of the differential Heun equation. We illustrate the use of this approach in two contexts: the representation theory of $O(3)$ and the computation of the entanglement entropy for free Fermions on the Krawtchouk chain.
