Theory of order and fluctuations in quantum materials

材料研究部资助本奖项用于强相互作用电子系统物理学的理论研究和教育。研究这些系统中的涌现特性，即系统作为一个整体显示但不具有组成部分特征的特性，是理论物理学的中心重点之一，也是目前广泛的子领域的一个关键领域，包括凝聚态物质、弦理论和量子引力、冷原子凝聚物和量子信息论。更一般地说，量子材料在一系列更广泛的应用科学中发挥着越来越重要的作用，因此对这些问题的更多理解也有可能影响科学和技术的更广泛发展。该领域的理论工作范围从高度集中的“微观”研究，试图提供对特定有趣材料的特定特性的定量理解，到更抽象的简单模型研究，揭示量子材料可能的定性行为。该奖项支持的大部分工作属于后一种类型。解析方法和新开发的数值方法将用于计算许多相互作用电子的范式模型的平衡和近平衡性质。这些知识可以使我们能够定性地接触到迄今为止被证明过于复杂而无法从更微观的角度来理解的材料的特性。所有拟议的研究将与博士生和博士后学者合作进行。所提出的研究的理论精确性和现象学相关性的结合，使它们成为培养未来凝聚态理论家的理想选择，更一般地说，是培养能够在广泛的领域解决复杂、开放式问题的学者的理想选择。技术概述材料研究部资助本奖项用于强相互作用电子系统物理学的理论研究和教育。强相互作用电子系统的显著特征之一是相互竞争或共存的秩序形式之间的复杂相互作用，包括磁性、超导性和电子液晶秩序。了解这些有序趋势之间的相互关系以及与之相关的波动可能是理解高度相关量子材料（包括各种高温超导体）物理学的关键。尽管这些材料的化学和结构各不相同，但它们新兴的低能物理的许多方面在性质上是相似的。在零温度量子临界点附近（电子顺序作为外部调谐参数的函数开始），微观物理被平均，从而产生普遍标度行为。更一般地说，许多感兴趣的材料显示出令人惊讶的简单标度定律，例如电阻率与温度的线性依赖关系，在可能或可能不受“附近”量子临界点影响的广泛范围内。在这项建议中，PI将对相关材料的顺序和波动相互作用的定性方面进行理论调查。这项工作将集中在简单的模型上，这些模型可以阐明强相关电子系统的一般行为。研究方向包括：1)确定量子蒙特卡罗（DQMC）方法将用于研究不受费米子负号问题影响的相互作用电子模型，从而可以在广泛的温度和系统尺寸范围内有效地求解。大部分的工作将致力于金属系统中的量子临界模型。此外，电子与声子强相互作用的问题，这是传统超导体物理学的核心，将被重新审视，以理解，除其他外，是什么限制了最高超导转变温度。2)将研究传统的金属近自由电子理论所不能描述的电子传递的新机制。特别是，PI将识别固体中电子流体动力学行为的机制，即作为具有几乎守恒动量和能量的局部平衡集体“流体”。此外，“坏金属”输运制度，其中材料的电阻率太高，无法用几乎独立的准粒子模型来解释，将在简单的理论模型中进行探索，可以控制在一定的限度内。所有拟议的研究将与博士生和博士后学者合作进行。所提出的研究的理论精确性和现象学相关性的结合，使它们成为培养未来凝聚态理论家的理想选择，更一般地说，是培养能够在广泛的领域解决复杂、开放式问题的学者的理想选择。

NONTECHNICAL SUMMARYThe Division of Materials Research funds this award on theoretical research and education in the physics of strongly interacting electron systems. The study of emergent properties in these systems, i.e. properties that the system displays as a whole but which are not characteristic of the constituents, is one of the central thrusts of theoretical physics, and currently a key area of inquiry in a broad range of subfields including condensed matter, string theory and quantum gravity, cold-atom condensates, and quantum information theory. More generally, quantum materials play an increasingly important role in a range of more applied sciences, so increased understanding of these problems has the potential to influence broader developments in science and technology as well. Theoretical work in this field ranges from highly focused "microscopic" studies that attempt to provide a quantitative understanding of specific properties of particular interesting materials, to more abstract studies of simple models that shed light on the possible qualitative behaviors of quantum materials. The bulk of the work that will be supported by this award is of the latter variety. Both analytic and newly developed numerical methods will be deployed to compute the equilibrium and near-equilibrium properties of paradigmatic models of many interacting electrons. That knowledge could enable qualitative contact with measured properties of materials that have so far proven too complex to be understood from a more microscopic perspective.All of the proposed research will be carried out in collaboration with PhD students and post-doctoral scholars. The combination of theoretical precision and phenomenological relevance of the proposed studies makes them ideal for training future condensed matter theorists, and more generally for producing scholars able to grapple with complex, open-ended problems in a broad range of venues.TECHNICAL SUMMARYThe Division of Materials Research funds this award on theoretical research and education in the physics of strongly interacting electron systems. One of the striking characteristics of systems of strongly interacting electrons is the complex interplay between competing or coexisting forms of order including magnetism, superconductivity, and electronic liquid crystalline order. Understanding the inter-relations between these ordering tendencies and the fluctuations associated with them may well be the key to understanding the physics of highly correlated quantum materials, including various high-temperature superconductors. Many aspects of the emergent low-energy physics of such materials are qualitatively similar despite their chemical and structural diversity. In the vicinity of a zero temperature quantum critical point (where an electronic order onsets as a function of an external tuning parameter), the microscopic physics is averaged out, giving rise to universal scaling behavior. More generally, many of the materials of interest show surprisingly simple scaling laws, such as a linear dependence of the resistivity on temperature, over broad regimes which may or may not be influenced by a "nearby" quantum critical point.In this proposal, the PI will undertake a theoretical investigation of the qualitative aspects of the interplay of order and fluctuations in correlated materials. The work will focus on simple models that can illuminate the generic behavior of systems of strongly correlated electrons. Among the directions to be pursued are:1) Determinantal quantum Monte Carlo (DQMC) methods will be employed to study models of interacting electrons that do not suffer from the fermion minus sign problem, and can thus be solved efficiently in a broad range of temperatures and system sizes. A large part of the effort will be devoted to models of quantum criticality in metallic systems. In addition, the problem of electrons interacting strongly with phonons, which is at the heart of the physics of conventional superconductors, will be revisited in order to understand, among other things, what limits the maximum superconducting transition temperature.2) Novel regimes of electron transport, not described by the traditional nearly-free-electron theory of metals, will be investigated. In particular, the PI will identify regimes in which electrons in solids behave hydrodynamically, i.e. as a locally-equilibrated collective "fluid" with a nearly-conserved momentum and energy. In addition, the "bad metal" transport regime, where the resistivity of a material is too high to be accounted for by a model of nearly-independent quasi-particles, will be explored in simple theoretical models that can be controlled in certain limits.All of the proposed research will be carried out in collaboration with PhD students and post-doctoral scholars. The combination of theoretical precision and phenomenological relevance of the proposed studies makes them ideal for training future condensed matter theorists, and more generally for producing scholars able to grapple with complex, open-ended problems in a broad range of venues.