We present a unified factorization framework for driven anisotropic Rabi-Stark Hamiltonians using affine spin-pencil theory. The method yields exact zero-energy ground states and determines exceptional parameter values for finite-polynomial eigenstates.
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Unified algebraic framework reveals Holstein-Primakoff and Dyson-Maleev transformations emerge as factorizations of the same structure, bridging spin algebra and bosonic representations—advancing understanding of quantum magnetism, simulation, and computing.
