Self-Consistent Field Theory for Correlated Electrons in Solids

在自洽场近似的框架下，对固体中相关电子的性质进行计算研究。这种近似构成了哈特里-福克理论对强相互作用和大电子涨落系统的自然推广，包括铜高温超导体。自洽场方法提供了精确对角化或模拟等数值技术的半解析替代方法。提出的研究集中于将自洽场方法扩展到(a)具有非平凡单元胞结构的晶格模型，包括描述铜超导体的多轨道模型；(b)具有无限范围库仑相互作用的晶格模型。此外，提出了一种改进一般两粒子相关函数中非局部顶点处理的研究方案。将研究新的计算技术来处理强相互作用的电子系统，而现有的方法不适用于这些系统。特别有趣的是，这些新技术将应用于理解高温超导体的问题。＊＊＊

9520636 Bickers Computational research will be conducted on the properties of correlated electrons in solids within the framework of self-consistent field approximations. Such approximations constitute the natural generalization of Hartree-Fock theories to systems with strong interactions and large electronic fluctuations, including the cuprate high- temperature superconductors. The self-consistent field approach provides a semi-analytical alternative to numerical techniques like exact diagonalization or simulation. The research proposed concentrates on the extension of the self- consistent field approach to (a) lattice models with nontrivial unit-cell structure, including multi-orbital models describing the cuprate superconductors; and (b) lattice models with infinite-range Coulomb interactions. In addition, a program of study is proposed to improve the treatment of nonlocal vertices in general two-particle correlation functions. %%% New computational techniques will be investigated to deal with systems of electrons which interact strongly and for which existing methods are not applicable. Of particular interest, these new techniques will be applied to the problem of understanding high-temperature superconductors. ***