Time-dependent local Green’s operator and its applications to manganites

An algorithm is presented to calculate the electronic local time-dependent Green’s operator for manganites-related Hamiltonians. This algorithm is proved to scale with the number of states in the Hilbert space to the 1.55 power, N is capable 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 results for the manganites phase diagram for the spatial dimension D=3 and half-filling on a 12×12×12 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.