Combination of First Principle Electronic Structure Theory and Many Electron Theory

为了将第一性原理电子结构理论和多电子理论结合起来，我们研究了以下几个问题：(1)LDA+U方法的发展及其应用：该方法在密度泛函理论的框架内考虑了电子-电子相互作用引起的电荷和自旋密度的大起伏的影响。我们研究了La_&lt；1-x&gt；SrxNiO_4的电子结构，认为该体系不能用LDA或LDA+U来处理，目前正在用严格的多体哈密顿量对角化方法进行研究。(2)GW近似的发展及其应用：GW近似是许多电子微扰理论的最低阶处理。我们开发了偏置法、广义乘积基方法和程序代码的并行化。将该方法应用于HfO和A型反铁磁LaMnO_3。到目前为止，A型反铁磁LaMnO_3实际上太大，不能用GW近似。我们使用OpenMT开发了并行代码。计算得到的光谱、带隙和磁矩与实验结果吻合较好。(3)DMFT+LDA：DMFT(动态平均场理论)是多电子理论，是为了讨论金属-绝缘体相变而发展起来的。这一理论揭示了在M-I相变附近由于电荷和自旋涨落引起的相干动力学。在多轨道情况下，我们利用迭代微扰理论将DMFT和LDA相结合，讨论了M-I跃迁的U/W(库仑相互作用与带宽之比)的临界值。文中还将IPT框架推广到S、p和d频段的情况。这是一种很有前途的方法，因为在现阶段，蒙特卡罗方法对一般哈密顿量的应用和对LDA的应用还没有完全建立起来。

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.