CAREER: Novel states of correlated quantum matter in numerical simulations, field theories and natural systems

技术总结这个职业奖项支持理论和计算研究和教育，旨在提高我们对凝聚态物理微观模型的非微扰方面的理解，以及它们在描述复杂材料实验中的应用。从理论上透彻地理解凝聚态物理的微观量子模型在零温度下可能实现的阶段是基础物理学的一个重要前沿。这一理解在自然系统中有着广泛的应用，特别是与近年来在实验室合成的大量复杂材料的丰富行为有关。不幸的是，相互作用的量子多体问题往往是难以解决的，无论是在分析上还是在数值上，如果不进行不受控制的近似。量子多体物理非微扰解的一个令人兴奋的发展前景是，在大晶格上以无偏见的方式对微观模型进行数值模拟(使用量子蒙特卡罗、密度矩阵重整化群和精确对角化等方法)与场论方法(如重整化群、大N和epsilon展开和平均场理论)的强大结合。该奖项支持所有这些方向的研究：数值模拟、场论方法和实验数据分析，以解决关联量子凝聚态物理中的新问题。主要主题包括：1)二维反铁磁体中的量子临界性，2)理解复杂材料中受挫磁性的实验，3)强关联系统中杂质的作用，4)发展新的QMC算法的全局更新方案，5)改进我们对QMC“符号问题”的理解，扩大没有这个问题的模型的类别。这个奖项支持本科生和研究生以及博士后研究员的教育机会。PI计划为肯塔基大学的研究生和高级本科生开发一门新的计算物理课程。他将参加一个旨在通过在他的小组中为教育专业的学生提供研究机会来改善高中物理教学的项目。PI将与附近Berea学院的一名同事合作，开展一系列项目(讲座、座谈、物理日活动)，以促进两所机构之间的本科生交流。该学院三分之一的学生来自少数民族。非技术总结这个职业奖项支持理论研究和教育，旨在提高我们对具有非常大的、实际上是无限数量的粒子的量子力学系统的理解，以及如何使用这些知识来解释复杂固态材料的不寻常行为。许多相互作用的粒子的量子物理构成了我们理解复杂材料性质的基础，世界各地的实验室正在合成越来越多的复杂材料。预测新材料的性质和与新材料相关的现象的能力在寻找未来技术的基石方面可以发挥关键作用。磁性出现在一些复杂的材料中，与温度降低时自发形成的内部磁场的自组织模式有关。使用量子多体系统的理论方法，PI将讨论在接近绝对零度的温度下在各种复杂材料中形成的磁性的性质，以及磁性如何被量子力学起源的涨落破坏。这个项目的重点是开发计算方法并应用它们使并行计算机能够提供对量子力学系统的基本见解，特别是涉及复杂材料中电子的虚拟宇宙的令人惊叹的性质和现象。该奖项支持本科生和研究生以及博士后研究员的教育机会。PI计划为肯塔基大学的研究生和高级本科生开发一门新的计算物理课程。他将参加一个旨在通过在他的小组中为教育专业的学生提供研究机会来改善高中物理教学的项目。PI将与附近Berea学院的一名同事合作，开展几个项目，导致两所机构之间的本科生交流。Berea学院三分之一的学生来自少数民族。

TECHNICAL SUMMARYThis CAREER award supports theoretical and computational research and education aimed at improving our understanding of non-perturbative aspects of microscopic models of condensed matter physics and their applications to the description of experiments on complex materials.A thorough theoretical understanding of the possible phases that microscopic quantum models of condensed matter physics can realize at zero temperature is an important frontier in fundamental physics. This understanding has vast applications to natural systems, especially relevant to the rich behavior of the large number of complex materials that have been synthesized in laboratories in recent years. Unfortunately, interacting quantum many body problems are often intractable either analytically or numerically without making uncontrolled approximations. An exciting prospect for progress in non-perturbative solutions of quantum many body physics is the powerful combination of numerical simulations of microscopic models in an unbiased way on large lattices (using methods such as quantum Monte Carlo, density matrix renormalization group and exact diagonalization), with field theoretic methods (such as renormalization group, large-N and epsilon−expansions and mean field theory). This award supports research at the interface of all these directions: numerical simulations, field theoretic methods, and analysis of experimental data, to address novel problems in correlated quantum condensed matter physics. Key topics include:1) Quantum criticality in two-dimensional anti-ferromagnets,2) Understanding experiments on frustrated magnetism in complex materials,3) The role of impurities in strongly correlated systems,4) Development of new global update schemes for QMC algorithms,5) Improvement of our understanding of the "sign problem" of QMC and broadening the class of models that are free of this problem.This award supports educational opportunities for undergraduate and graduate students as well as postdoctoral fellows. The PI plans to develop a new course on computational physics for graduate and advanced undergraduate students at the University of Kentucky. He will participate in a program that is aimed at improving high school physics instruction by offering Education majors research opportunities in his group. Working in collaboration with a colleague at the nearby Berea College, where a third of the students are from ethnic minorities, the PI will carry out a number of projects (lectures, colloquia, Physics day activities) that will result in undergraduate student exchange between the two institutions. NON-TECHNICAL SUMMARYThis CAREER award supports theoretical research and education aimed at improving our understanding of quantum mechanical systems with a very large, practically infinite, number of particles and how this knowledge may be used to explain the unusual behavior of complex solid state materials. Quantum physics of many interacting particles forms the basis of our understanding of the properties of complex materials, a growing number of which are being synthesized in laboratories all over the world. The ability to predict the properties of new materials and new materials-related phenomena can play a crucial role in the search for the building blocks of future technologies. Magnetism appears in some complex materials and relates to spontaneously developing self-organized patterns of internal magnetic fields when the temperature is lowered. Using theoretical methods for quantum many body systems, the PI will address both the nature of the magnetism that develops in a variety of complex materials at temperatures close to the absolute zero of temperature and how magnetism can be destroyed by fluctuations of quantum mechanical origin. This project includes a focus on developing computational methods and applying them to enable parallel computers to provide fundamental insight into quantum mechanical systems, particularly the amazing properties and phenomena that involve a virtual universe of electrons in complex materials.This award supports educational opportunities for undergraduate and graduate students as well as postdoctoral fellows. The PI plans to develop a new course on computational physics for graduate and advanced undergraduate students at the University of Kentucky. He will participate in a program that is aimed at improving high school physics instruction by offering Education majors research opportunities in his group. Working in collaboration with a colleague at the nearby Berea College, where a third of the students are from ethnic minorities, the PI will carry out several projects that will result in undergraduate student exchange between the two institutions.