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.
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials
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abstract
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the restrictions either to the odd or to the even points of the complete orthogonality lattice. This is exploited to design very efficient inverse problem algorithms for the reconstruction of persymmetric Jacobi matrices from spectral points. Isospectral deformations of such matrices are also considered. Expressions for the associated polynomials and their weights are obtained in terms of the undeformed entities.
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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.