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Heun operator of Lie type and the modified algebraic Bethe ansatz
Pierre-Antoine Bernard, Nicolas Crampe, Dounia Shaaban Kabakibo +1
The generic Heun operator of Lie type is identified as a certain -Gaudin magnet Hamiltonian in a magnetic field. By using the modified algebraic Bethe ansatz introduced to diag…
Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coeffici…
Entanglement of Free Fermions on Hadamard Graphs
Nicolas Crampe, Krystal Guo, Luc Vinet
Free Fermions on vertices of distance-regular graphs are considered. Bipartition are defined by taking as one part all vertices at a given distance from a reference vertex. The gro…
Sklyanin-like algebras for (-)linear grids and (-)para-Krawtchouk polynomials
Geoffroy Bergeron, Julien Gaboriaud, Luc Vinet +1
S-Heun operators on linear and -linear grids are introduced. These operators are special cases of Heun operators and are related to Sklyanin-like algebras. The Continuous Hahn a…
The Heun-Racah and Heun-Bannai-Ito algebras
Geoffroy Bergeron, Nicolas Crampé, Satoshi Tsujimoto +2
This paper introduces and studies the Heun-Racah and Heun-Bannai-Ito algebras abstractly and establishes the relation between these new algebraic structures and generalized Heun-ty…
Entanglement in Fermionic Chains and Bispectrality
Nicolas Crampé, Rafael I. Nepomechie, Luc Vinet
Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a…