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New Developments in the Green's-Function Method and Construction of the Strong-Coupling Theory for Superconductivity with Vertex Corrections

格林函数方法的新进展及顶点修正超导强耦合理论的构建

基本信息

批准号：
10640363
负责人：
TAKADA Yasutami
金额：
$ 0.38万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

In order to illuminate fundamental physics in dynamical processes in a strongly-correlated system, I propose a theory of twofold hierarchy The first stage is to set up a firm framework to provide exact results without attention to feasibility of computation and the second one is to introduce a relevant approximation to the key quantity in the framework with taking full account of available resources of computation. Since I have already established the theory of the self-energy revision operator F for the first stage, the main objective of this study is the second stage, namely, to obtain a good approximation to F.The simplest approximation is the gauge-invariant self-consistent (GISC) method in which I neglect the vector vertex function ΓィイD2νィエD2 in relating the scalar vertex function Γ with the self-energy Σ through the Ward identity. I have improved on this GISC systematically by introducing the ratio function R, defined as the ratio between Γ and the longitudinal part of ΓィイD2νィエD2. I exploit its asymptotic properties in various limits to construct a good approximate form for R.For its illustration, I apply this algorithm to the electron gas and find the following : (i) Near the Fermi surface, RPA is found to provide rather accurate results because of the strong cancellation between Γ and Σ due to the Panli principle; (ii) it is not the case for the processes far from the Fermi surface; and (iii) a strong lower-energy shift is observed in the dynamic structure factor owing to the attractive electron-hole excitonic multiple scatterings. I shall apply the same method to real crystals.As for superconductivity, I develop a theory on the GISC level and investigated the validity of the conventional Eliashberg theory in various aspects. I shall extend the theory so as to provide more accurate results with full attention to the role of Nambu-Goldstone modes in Γ.

为了阐明强关联系统动力学过程中的基本物理问题，本文提出了一个两重层次的理论。第一阶段是建立一个可靠的框架，在不考虑计算可行性的情况下提供精确的结果;第二阶段是在充分考虑可用计算资源的情况下，对框架中的关键量引入一个相应的近似。由于我已经建立了第一阶段的自能修正算子F的理论，因此本研究的主要目标是第二阶段，即，最简单的近似是规范不变自洽（GISC）方法，其中我在将标量顶点函数Γ与自洽函数联系起来时忽略了向量顶点函数通过沃德身份获取能量通过引入比值函数R，我系统地改进了这个GISC，定义为Γ与Γ D2ν D2的纵向部分之间的比值。为了说明这一点，我们将该算法应用于电子气，发现：（i）在费米面附近，由于Panli原理的存在，使得Γ和π之间存在强的相互抵消，RPA可以提供相当精确的结果;（ii）在远离费米面的情况下，RPA不能提供精确的结果;以及（iii）由于有吸引力的电子-空穴激子多重散射，在动态结构因子中观察到强烈的低能位移。我将把同样的方法应用于真实的晶体，对于超导性，我发展了一个GISC水平的理论，并从各个方面研究了传统Eliashberg理论的有效性。我将扩展理论，以便提供更精确的结果，并充分注意Nambu-Goldstone模在Γ中的作用。