Combination of First Principle Electronic Structure Theory and Many Electron Theory

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We have investigated the following topics in order to combine the first principle electronic structure theory and the many electron theory.(1)Development of LDA+U method and its applications : This method includes, within the framework of the density functional theory, the effects of large fluctuation of charge and spin densities due to electron-electron interactions. We studied the electronic structure of La_<1-x>SrxNiO_4. We concluded that this system could not be treated by LDA or LDA+U and now is being investigated by the method of rigorous diagonalization of the many-body Hamiltonian.(2)Development of the GW Approximation and its applications : GW approximation is the lowest order treatment of many electron perturbation theory. We developed the off-set method, the generalized product basis method, and the parallelization of program code. The method is applied to HfO and A-type antiferromagnetic LaMnO_3. Up to now, A-type antiferromagnetic LaMnO_3 is actually too large for the GW approximation. We developed the parallel code by using OpenMT. The resultant spectrum, band gap and magnetic moment show a good agreement with experimental ones. We also calculated the electron-electron interaction for both on-site and off-site on Mn atoms as a function of excitation energy.(3)DMFT+LDA : DMFT (Dynamical Mean Field Theory) is the many electron theory and has been developed in order to discuss the metal-insulator transition. This theory shows the coherent dynamics due to charge and spin fluctuation near M-I transition. We combine the DMFT with the LDA with a help of the Iterative Perturbation Theory in multi-orbital case and discussed the critical values of U/W (the ratio of Coulomb interaction and band width) for the M-I transition. Also the IPT framework is generalized to the case of s, p and d bands. This is very promising method because, at the present stage, the application of the Monte Calro method to general Hamiltonian an that of the LDA is not fully established.