Theory of order and fluctuations in quantum materials

非技术总结材料研究部资助强相互作用电子系统物理学的理论研究和教育奖。对这些系统的涌现性质的研究，即系统作为一个整体表现出来但不是组成成分的特征的性质，是理论物理的中心推动力之一，目前是包括凝聚态、弦理论和量子引力、冷原子凝聚体和量子信息论在内的广泛子领域的关键研究领域。更广泛地说，量子材料在一系列更多的应用科学中发挥着越来越重要的作用，因此对这些问题的理解的加深也有可能影响更广泛的科学和技术发展。这一领域的理论工作包括从试图提供对特定感兴趣材料的特定性质的定量理解的高度集中的“微观”研究，到揭示量子材料可能的质量行为的更抽象的简单模型研究。该奖项将支持的大部分工作属于后一种类型。解析方法和新发展的数值方法将被用来计算多个相互作用电子的聚合模型的平衡和近平衡性质。这一知识可以使人们定性地接触到材料的测量性质，这些材料迄今被证明过于复杂，无法从更微观的角度加以理解。所有拟议的研究都将与博士生和博士后学者合作进行。拟议研究的理论精度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，更广泛地说，它们可以培养出能够在广泛的场合解决复杂的、开放的问题的学者。技术总结材料研究部资助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有序形式之间的复杂相互作用，包括磁性、超导和电子液晶有序。了解这些有序趋势和与之相关的涨落之间的相互关系，很可能是理解包括各种高温超导体在内的高度关联量子材料物理的关键。尽管这些材料的化学和结构不同，但它们的新兴低能物理的许多方面在性质上是相似的。在零温量子临界点附近(电子有序作为外部调谐参数的函数)，微观物理被平均化，从而产生普遍的标度行为。更广泛地说，许多感兴趣的材料表现出令人惊讶的简单的标度定律，例如在可能或可能不受附近的量子临界点影响的广泛区域内，电阻率与温度的线性关系。在这个建议中，PI将对相关材料中有序和涨落相互作用的定性方面进行理论研究。这项工作将专注于简单的模型，这些模型可以解释强关联电子系统的一般行为。1)行列式量子蒙特卡罗(DQMC)方法将被用来研究相互作用电子的模型，这些模型不存在费米子减号问题，因此可以在广泛的温度和系统尺寸范围内有效地求解。很大一部分工作将致力于金属系统中的量子临界性模型。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的核心，将被重新讨论，以便除其他外，了解是什么限制了最高超导转变温度。2)将研究传统的近自由电子金属理论没有描述的电子传输的新制度。特别是，PI将确定固体中电子的流体动力学行为的区域，即作为具有近乎守恒的动量和能量的局部平衡的集体“流体”。此外，“坏金属”传输机制，即材料的电阻率太高，不能用几乎独立的准粒子模型来解释，将在简单的理论模型中探索，可以控制在一定的范围内。所有拟议的研究都将与博士生和博士后学者合作进行。拟议研究的理论精确度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，更广泛地说，它们适合培养能够在广泛的场所解决复杂的、开放的问题的学者。

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.