An algorithm is presented to calculate the electronic local time-dependent Greens operator for manganites-related hamiltonians. This algorithm is proved to scale with the number of states $N$ in the Hilbert-space to the 1.55 power, is able of parallel implementation, and outperforms computationally the Exact Diagonalization (ED) method for clusters larger than 64 sites (using parallelization). This method together with the Monte Carlo (MC) technique is used to derive new results for the manganites phase diagram for the spatial dimension D=3 and half-filling on a 12x12x12 cluster (3456 orbitals). We obtain as a function of an insulating parameter, the sequence of ground states given by: ferromagnetic (FM), antiferromagnetic AF-type A, AF-type CE, dimer and AF-type G, which are in remarkable agreement with experimental results.
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