A novel analytic spin chain model with fractional revival

Abstract

New analytic spin chains with fractional revival are introduced. Their nearest-neighbor couplings and local magnetic fields correspond to the recurrence coefficients of para-Racah polynomials which are orthogonal on quadratic bi-lattices. These models generalize the spin chain associated to the dual-Hahn polynomials. Instances where perfect state transfer also occurs are identified.

8 pages, 3 figures

References in corpus (6)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Mirror Inversion of Quantum States in Linear Registers
• Coherent Quantum Transport in Photonic Lattices
• Experimental Perfect Quantum State Transfer
• Perfect wave-packet splitting and reconstruction in a one-dimensional lattice
• Fractional revivals of quantum state in tight-binding chain

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• Single- to many-body crossover of a quantum carpet
• A classical model for perfect transfer and fractional revival based on $q$-Racah polynomials
• Sklyanin-like algebras for ($q$-)linear grids and ($q$-)para-Krawtchouk polynomials
• Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
• Analytic "Newton's cradles" with perfect transfer and fractional revival
• Orthogonal polynomials and the deformed Jordan plane
• Quantum carpets from Gaussian sum theory
• Effective non-local parity-dependent couplings in qubit chains