Two new families of inhomogeneous XY spin chains are constructed whose spectra and eigenvectors follow exactly from the B2-contiguity relations of q-Racah polynomials.
Contiguity relations for finite families of orthogonal polynomials in the Askey scheme
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abstract
This paper classifies the contiguity relations for finite families of polynomials within the ($q$-)Askey scheme. The necessary and sufficient conditions for the existence of these contiguity relations are presented first. These conditions are then solved, yielding a comprehensive list of contiguity relations for these various families of polynomials. Furthermore, we demonstrate that all contiguity relations correspond to spectral transforms.
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Exactly solvable inhomogeneous XY spin chain
Two new families of inhomogeneous XY spin chains are constructed whose spectra and eigenvectors follow exactly from the B2-contiguity relations of q-Racah polynomials.