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Matrix diagonalization has long been a setback in the numerical simulation ofthe magnetic resonance spectra of multispin systems since the dimension of theHilbert space of such systems grows exponentially with the number of spins -- aproblem commonly referred to as the "curse of dimensionality". In this paper,we propose two mathematical instruments which, when harmoniously combined,could greatly help surmount to a fair degree and in a systematic manner thecurse of dimensionality. These are: 1) the Holstein-Primakoff bosons and 2)what we have termed the "index compression maps". These two allow a bijectivemapping of (multi)spin states to integers. Their combination leads to the blockdiagonalization of the multispin Hamiltonian, thus a computationally exact wayof diagonalizing the latter but which also reduces significantly thecomputational cost. We also show that the eigenvectors and eigenvalues of theLiouvillian operator can be easily determined once those of the relatedmultispin Hamiltonian are known. Interestingly, the method also enables ananalytical characterization of the multispin Hilbert space -- a feat hardlyattainable with other approaches.  We illustrate the method here by showing how a general static isotropicmultispin Hamiltonian could be exactly diagonalized with very lesscomputational cost. Nonetheless, we emphasize that the method could be appliedto study numerous quantum systems defined on finite Hilbert spaces and embodiedwith at most pairwise interactions.

Magnetic Resonance, Index Compression Maps and the Holstein-Primakoff  Bosons: Towards a Polynomially Scaling Exact Diagonalization of Isotropic  Multispin Hamiltonians