Theory of order and fluctuations in quantum materials

非技术性总结材料研究部资助这个奖项的理论研究和教育在强相互作用的电子系统的物理。对这些系统中突现性质的研究，即系统作为一个整体所表现出的性质，但不是组成部分的特征，是理论物理学的中心目标之一，目前也是包括凝聚态、弦理论和量子引力、冷原子凝聚和量子信息理论在内的广泛子领域的一个关键研究领域。更广泛地说，量子材料在一系列更应用的科学中发挥着越来越重要的作用，因此对这些问题的理解也有可能影响科学和技术的更广泛发展。这一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性质的定量理解，到对简单模型的更抽象的研究，揭示量子材料可能的定性行为。 该奖项将支持的大部分工作属于后一种。 分析和新开发的数值方法将被部署来计算许多相互作用的电子的范例模型的平衡和近平衡特性。 这些知识可以使材料的测量特性与迄今为止被证明过于复杂而无法从更微观的角度理解的材料的测量特性进行定性联系。所有拟议的研究都将与博士生和博士后学者合作进行。 理论精度和现象学的建议研究的相关性相结合，使他们成为理想的培训未来凝聚态理论家，更普遍地为生产学者能够与复杂的，开放式的问题，在广泛的views.Technical总结材料研究部基金这个奖项的理论研究和教育在强相互作用的电子系统的物理。强相互作用电子系统的显著特征之一是竞争或共存的有序形式之间的复杂相互作用，包括磁性，超导性和电子液晶有序。理解这些有序趋势和与之相关的波动之间的相互关系可能是理解高度相关量子材料物理学的关键，包括各种高温超导体。尽管这些材料的化学和结构多样性，但它们的新兴低能物理学的许多方面在性质上是相似的。在零温度量子临界点附近（其中电子序作为外部调谐参数的函数开始），微观物理被平均化，引起普遍的标度行为。更一般地说，许多感兴趣的材料表现出令人惊讶的简单的标度律，如电阻率对温度的线性依赖性，在广泛的制度，可能会或可能不会受到影响的“附近”的量子criticalpoint.In这个建议，PI将承担相关材料的顺序和波动的相互作用的定性方面的理论研究。这项工作将集中在简单的模型，可以照亮强相关电子系统的一般行为。 其中要追求的方向是：1）确定性量子蒙特卡罗（DQMC）方法将被用来研究相互作用的电子模型，不受费米子负号问题，因此可以有效地解决在广泛的温度和系统尺寸。很大一部分工作将致力于金属系统中的量子临界模型。此外，电子与声子强烈相互作用的问题，这是传统超导体物理学的核心，将被重新审视，以了解，除其他事项外，是什么限制了最大超导转变温度。特别是，PI将确定其中固体中的电子表现为流体动力学的制度，即作为具有接近守恒的动量和能量的局部平衡的集体“流体”。此外，对于材料的电阻率太高，无法用近似独立的准粒子模型来解释的“坏金属”输运状态，将在能够控制在一定限度内的简单理论模型中进行探索。所有研究都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，更普遍地说，是培养能够在广泛的场合处理复杂的、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.