Self-Consistent Field Theory for Correlated Electrons in Solids

9520636 Bickers计算研究将在自洽场近似的框架内对固体中相关电子的性质进行研究。 这种近似构成了哈特里-福克理论对具有强相互作用和大电子涨落的系统的自然推广，包括铜氧化物高温超导体。 自洽场方法提供了一个半解析的替代数值技术，如精确对角化或模拟。 本文的研究主要集中在将自洽场方法推广到（a）具有非平凡单胞结构的晶格模型，包括描述铜氧化物超导体的多轨道模型;（B）具有无限程库仑相互作用的晶格模型。 此外，还提出了一个改进一般两粒子关联函数中非局域顶点处理的研究方案。 将研究新的计算技术，以处理相互作用强烈的电子系统，现有的方法不适用。 特别令人感兴趣的是，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. ***