Geodesic
Inhomogeneous isotropic quantum spin chain associated with the difference Lamé equation
Forum of Mathematics, Sigma, Tome 12 (2024)

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The spectrum and orthogonal eigenbasis are computed of a tridiagonal matrix encoding a finite-dimensional reduction of the difference Lamé equation at the single-gap integral value of the coupling parameter. This entails the exact solution, in terms of single-gap difference Lamé wave functions, for the spectral problem of a corresponding open inhomogeneous isotropic $XY$ chain with coupling constants built from elliptic integers. 
@article{10_1017_fms_2024_88,
     author = {Jan Felipe van Diejen},
     title = {Inhomogeneous isotropic quantum spin chain associated with the difference {Lam\'e} equation},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {12},
     year = {2024},
     doi = {10.1017/fms.2024.88},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.88/}
}
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Jan Felipe van Diejen. Inhomogeneous isotropic quantum spin chain associated with the difference Lamé equation. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.88

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