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- W2896052281 abstract "Matrix diagonalization has long been a setback in the numerical simulation of the magnetic resonance spectra of multispin systems since the dimension of the Hilbert space of such systems grows exponentially with the number of spins -- a problem commonly referred to as the of 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 the curse of dimensionality. These are: 1) the Holstein-Primakoff bosons and 2) what we have termed the index compression maps. These two allow a bijective mapping of (multi)spin states to integers. Their combination leads to the block diagonalization of the multispin Hamiltonian, thus a computationally exact way of diagonalizing the latter but which also reduces significantly the computational cost. We also show that the eigenvectors and eigenvalues of the Liouvillian operator can be easily determined once those of the related multispin Hamiltonian are known. Interestingly, the method also enables an analytical characterization of the multispin Hilbert space -- a feat hardly attainable with other approaches. We illustrate the method here by showing how a general static isotropic multispin Hamiltonian could be exactly diagonalized with very less computational cost. Nonetheless, we emphasize that the method could be applied to study numerous quantum systems defined on finite Hilbert spaces and embodied with at most pairwise interactions." @default.
- W2896052281 created "2018-10-26" @default.
- W2896052281 creator A5010900247 @default.
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- W2896052281 date "2018-03-28" @default.
- W2896052281 modified "2023-09-27" @default.
- W2896052281 title "Magnetic Resonance, Index Compression Maps and the Holstein-Primakoff Bosons: Towards a Polynomially Scaling Exact Diagonalization of Isotropic Multispin Hamiltonians" @default.
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