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Eigenvalue degeneracy relations for a fully connected isotropic spin network. (English) Zbl 1226.81035

Summary: We present and prove identities for the eigenvalue degeneracy of a fully connected spin network with isotropic spin coupling. Such a network has application to quantum information processing, especially for solid-state implementations, and in fact the qubit case with anisotropic coupling has been recently realized. One set of proofs and other relations for the case of qubits is given in the context of hypergeometric summation. We then generalize to arbitrary spin, using combinatorial arguments.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
34B45 Boundary value problems on graphs and networks for ordinary differential equations
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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