Spectral surgery on a uniform XX chain yields analytic spin chains that interpolate between uniform and Krawtchouk chains and achieve good-fidelity state transfer with bounded couplings.
q-Ultraspherical polynomials for q a root of unity
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abstract
Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of $q$-beta integrals of Ramanujan.
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Spectral surgery and high-fidelity quantum state transfer in $XX$ chains
Spectral surgery on a uniform XX chain yields analytic spin chains that interpolate between uniform and Krawtchouk chains and achieve good-fidelity state transfer with bounded couplings.