Algorithms on low energy spectra of the Hubbard model pertinent to molecular nanomagnets

Abstract

SummaryComputer supported design of materials with tailored properties is an important part of computational science so that developments of new effective algorithms is a key issue. Molecular magnetism deals with complex objects described by the quantum physics and their simulations come up against the computational constraints. In this work, we consider a numerical version of a recently developed hybrid approach that combines the ab initio DFT method with the exact diagonalization of the microscopic Hubbard model (HM). The latter avoids the prior perturbative framework but increases computing resources needed for solving the eigenvalue problem of the matrix representation of HM. We demonstrate that in the case of the ring‐shape molecular nanomagnets the computational demands can be curbed due to efficient numerical matrix construction algorithms provided. These algorithms pertain both to the calculation of the single nonzero matrix elements and to their localization in the final sparse matrix that is subsequently diagonalized. Their implementation executed on a simple six‐core‐computer system and the Mathematica environment leads to a significant gain in the computing time for the exemplary chromium‐based molecule denoted Cr, running the code sequentially. We claim, referring to the numerical diagonalization of the spin Hamiltonian matrices, that the parallelization flaws related to the high‐level programming approach can be all removed, porting the code to the appropriate HPC environment. A prospective implementation of the code, based on some dedicated and optimized mathematical libraries, will ultimately open a window for further applications of the Hubbard model in molecular magnetism.