Quantum Critical Phenomena and Non Fermi Liquid Physics

该补助金支持基础凝聚态物理学的理论研究。 理解相互作用的多粒子量子系统的行为是我们这个时代的核心智力挑战之一。 金属中的电子，除其他外，引起导电性，超导性和磁性，是一类特别重要和具有挑战性的相互作用的多粒子量子系统。 我们目前的理解是基于朗道的“费米液体理论”，该理论表明，在许多情况下，电子液体的明显复杂行为可以用弱相互作用的“准粒子”来理解。然而，多年来已经很清楚，朗道的图像未能描述广泛类别的金属的行为，包括那些显示出有趣和潜在重要行为的金属，如高温超导性和极大的磁阻。 本研究的目的是发展物理理解，沿着分析和计算技术，以理解传统概念无法充分描述的系统的“非费米液体”行为。本研究的一个中心焦点是“量子临界性”，即当材料的基态从一个相变为另一个相时发生的行为。 相变点附近的材料通常表现出大幅度、长范围、缓慢变化的波动，这在经验上已知会导致特别明显的非费米液体行为。 此外，这些波动的空间和时间范围很长，这意味着它们可以使用量子场论中已建立的技术进行分析研究。 这项研究的一个正在进行的主题是使用这些技术来研究强形式的非费米液体行为，目的是提取一般的见解和发展技术，可能会延续到其他问题。金属的一个特征是存在大密度的低位激发，这意味着波动通常是阻尼的-它们的能量被耗散到创建金属激发。 量子力学和耗散的相互作用是一个基本的和仍然不太清楚的问题：希望这项研究将导致新的见解的问题，无论是通过解决量子临界问题中出现的金属上下文，并通过新的计算相结合的分析技术上面提到的技术处理耗散对单个量子粒子的影响。 第二个重点的研究是发展和应用的数值技术确定热力学和动力学的系统和情况下没有充分描述的朗道的准粒子理论或其扩展。 在过去的十年中，与“动态平均场理论”的概念相关的理论发展表明，我们计算激发光谱和响应函数的能力有了显着的提高。 研究将扩展和改进这些技术，并将其应用于理解各种新材料的实验。学生和博士后同事将密切参与这项研究。%该补助金支持基础凝聚态物理学的理论研究。 理解相互作用的多粒子量子系统的行为是我们这个时代的核心智力挑战之一。 金属中的电子，除其他外，引起导电性，超导性和磁性，是一类特别重要和具有挑战性的相互作用的多粒子量子系统。 我们目前的理解是基于朗道的“费米液体理论”，该理论表明，在许多情况下，电子液体的明显复杂行为可以用弱相互作用的“准粒子”来理解。然而，多年来已经很清楚，朗道的图像未能描述广泛类别的金属的行为，包括那些显示出有趣和潜在重要行为的金属，如高温超导性和极大的磁阻。 本研究的目的是发展物理理解，沿着分析和计算技术，以理解传统概念无法充分描述的系统的“非费米液体”行为。学生和博士后同事将参与这项研究。*

This grant supports theoretical research into fundamental condensed matter physics. Understanding the behavior of interacting many-particle quantum systems is one of the central intellectual challenges of our time. Electrons in metals, which give rise among other things to conductivity, superconductivity and magnetism, are a particularly important and challenging class of interacting many-particle quantum system. Our present understanding is based on Landau's "Fermi liquid theory" which shows how, in many cases, the apparently complicated behavior of the electron liquid may be understood in terms of a picture of weakly interacting "quasiparticles." However, it has become clear over the years that Landau's picture fails to describe the behavior of a wide class of metals, including those displaying interesting and potentially important behavior such as high temperature superconductivity, and extremely large magnetoresistance. The research conducted here is aimed at developing the physical understanding, along with the analytical and computational techniques, needed to understand the "non-fermi-liquid" behavior of systems not adequately described by conventional concepts.One central focus of this research is "quantum criticality," the behavior occurring when the ground state of a material changes from one phase to another. Materials near a phase transition point typically exhibit large amplitude, long-ranged, slowly changing fluctuations, which are empirically known to lead to particularly pronounced non-fermi-liquid behaviors. Further, the long spatial and temporal range of these fluctuations means that they are amenable to analytical study using established techniques in quantum field theory. An ongoing theme of this research is the use of these techniques to study strong forms of non-fermi-liquid behavior with the goal of extracting general insights and developing techniques which may carry over to other problems.A characteristic feature of metals is the presence of a large density of low-lying excitations, which means that fluctuations are typically damped - their energy is dissipated into creating metallic excitations. The interplay of quantum mechanics and dissipation is a fundamental and still ill-understood issue: it is hoped that this research will lead to new insights into the issue, both via solution of quantum critical problems arising in the metallic context and via new calculations combining the analytical techniques mentioned above with techniques for dealing with effects of dissipation on a single quantum particle. A second focus of the research is the development and application of numerical techniques for determining thermodynamics and dynamics of systems and circumstances not adequately described by Landau's quasiparticle theory or its extensions. Theoretical developments over the past decade associated with the concept of "dynamical mean field theory" suggest dramatic improvements in our ability to calculate excitation spectra and response functions. Research will be undertaken into extending and improving these techniques, and in applying them to understand experiments in a wide range of novel materials.Students and postdoctoral associates will be closely involved in this research.%%%This grant supports theoretical research into fundamental condensed matter physics. Understanding the behavior of interacting many-particle quantum systems is one of the central intellectual challenges of our time. Electrons in metals, which give rise among other things to conductivity, superconductivity and magnetism, are a particularly important and challenging class of interacting many-particle quantum system. Our present understanding is based on Landau's "Fermi liquid theory" which shows how, in many cases, the apparently complicated behavior of the electron liquid may be understood in terms of a picture of weakly interacting "quasiparticles." However, it has become clear over the years that Landau's picture fails to describe the behavior of a wide class of metals, including those displaying interesting and potentially important behavior such as high temperature superconductivity, and extremely large magnetoresistance. The research conducted here is aimed at developing the physical understanding, along with the analytical and computational techniques, needed to understand the "non-fermi-liquid" behavior of systems not adequately described by conventional concepts.Students and postdoctoral associates will be involved in this research.***