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Journal Articles J.Math.Phys. Year : 2021

Heun operator of Lie type and the modified algebraic Bethe ansatz

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Pierre-Antoine Bernard
  • Function : Author
Dounia Shaaban Kabakibo
  • Function : Author
Luc Vinet
  • Function : Author

Abstract

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 also show that these Bethe roots are intimately associated with 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.
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Dates and versions

hal-03070671 , version 1 (11-10-2022)

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Pierre-Antoine Bernard, Nicolas Crampe, Dounia Shaaban Kabakibo, Luc Vinet. Heun operator of Lie type and the modified algebraic Bethe ansatz. J.Math.Phys., 2021, 62 (8), pp.083501. ⟨10.1063/5.0041097⟩. ⟨hal-03070671⟩
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