Theory of Highly Correlated Electronic Systems

该奖项支持基础凝聚态物理学的理论研究。 弱相互作用准粒子的费米液体描述已经非常成功地作为一个框架，用于处理各种晶体材料和固态器件中遇到的电子流体的性质，即使在电子-电子相互作用相当强的情况下，费米液体参数从它们的裸值强烈重整化。 然而，也有许多情况下，费米液体的方法定性失败：在单粒子谱函数中存在的任何色散特征在它们的宽度大于它们的平均值的意义上是过阻尼的系统，或者存在到具有与微观电子尺度相当的温度和能量尺度的对称性破缺状态的相变的系统，或者表现出与弱相互作用准粒子不一致的宏观行为，例如在低温极限下二维系统中的有限电阻，或者具有超过Ioffe-Regel极限的量值的金属（随着温度的增加而增加）介电常数。 非相互作用的电子作为良好发展的费米液体的适当范例，但简单的，可解的强相互作用的电子模型很少。 这里设想的研究的主要目的是获得控制良好的近似，甚至渐近精确的解决方案，以简单的模型，强相互作用的电子作为一个步骤，在填补这一空白。 更具体地说，提出研究电子之间具有纯排斥相互作用的模型，其中可以牢固地建立具有高转变温度的超导态的存在，并且可以可靠地估计转变温度。 这一研究对于阐明高温超导的机理具有重要意义。 在更唯象的水平上，建议研究电子微相分离的影响，这是强相关的“坏金属”中常见的现象，对各种宏观性质，如光学电导率和DC输运。 虽然这一努力的大部分是受到试图理解铜酸盐高温超导体的显着特性的启发，但也计划将相关想法应用于MOSFET中的低密度电子气体，以及其他高度相关的电子材料，如过渡金属氧化物和有机超导体。到目前为止，有许多高度相关的坏金属的例子，电子结构理论的传统方法失败了。 对这些材料有一个简单的、定性的理解是一个智力问题，就像“什么是金属？“高温超导性只是在这种材料中观察到的现象之一，但却是最令人兴奋的现象之一。这项工作将成为学生研究项目的丰富来源。 这些问题是明确定义的，并且具有直接的实验相关性，同时涉及许多身体物理学的大量方法的掌握。 该奖项支持基础凝聚态物理学的理论研究。 该主题是显示出强烈相互作用的电子的材料，这些电子产生的效应，如高温超导性，无法用当前理论来理解。 将遵循系统的程序来开发和解决模型，包括实验预测，这将有助于理解这些材料。 作为该项目的一部分，学生将接受凝聚态理论现代技术的培训。

This award supports theoretical research in fundamental condensed matter physics. The Fermi-liquid description of weakly interacting quasiparticles has been remarkably successful as a framework for treating the properties of the electron fluids encountered in a wide variety of crystalline materials and solid state devices, even where the electron-electron interactions are quite strong, and the Fermi liquid parameters are strongly renormalized from their bare values. However, there are also many cases where the Fermi liquid approach qualitatively fails: systems in which whatever dispersing feature there are in the single particle spectral functions are overdamped in the sense that their widths are larger than their mean, or where there are phase transitions to broken symmetry states with temperature and energy scales comparable to microscopic electronic scales, or that exhibit macroscopic behaviors that are inconsistent with weakly interacting quasiparticles, such as finite resistance in a two-dimensional system in the low temperature limit, or metallic(increasing with increasing temperature) resistivities with magnitudes in excess of the Ioffe-Regel limit. Non-interacting electrons serve as the appropriate paradigmatic for well developed Fermi liquids, but simple, solvable models of strongly interacting electrons are few and far between. It is the principle purpose of the research envisaged here to obtain well controlled approximate, or even asymptotically exact solutions to simple models of strongly interacting electrons as a step in filling this void. More particularly, it is proposed to study models with purely repulsive interactions between electrons in which the existence of a superconducting state with a high transition temperature can be firmly established and the transition temperature reliably estimated. This study is relevant to elucidating the mechanism of high temperature superconductivity. On a more phenomenological level, it is proposed to study the effects of electronic micro-phase-separation, a common occurrence in strongly correlated "bad metals," on various macroscopic properties such as the optical conductivity and DC transport. While much of this effort is inspired by an attempt to understand the remarkable properties of the cuprate high temperature superconductors, applications of related ideas to low density electron gases in MOSFET's, and to other highly correlated electronic materials, such as transition metal oxides and the organic superconductors, are also planned.There are, by now, many examples of highly correlated bad metals, where conventional approaches to the theory of electronic structure fail. Obtaining a simple, qualitative understanding of these materials is an intellectual question on par with, "What is a metal?" High temperature superconductivity is only one of the phenomena observed in such materials, but one of the most exciting.This work will serve as a fertile source of research projects for students. The problems are well defined, and of direct experimental relevance, while at the same time involving mastery of a large number of methods of many body physics. %%%This award supports theoretical research on fundamental condensed matter physics. The topic is materials which exhibit strongly interacting electrons which produce effects, such as high temperature superconductivity, that are unable to be understood with current theory. A systematic procedure will be followed to develop and solve models, including experimental predictions, which will contribute to the understanding of these materials. As part of this project, students will be trained in modern techniques of condensed matter theory.***