Novel phases of quantum matter in numerical simulations, field theory and materials

非技术性总结该奖项支持理论和计算研究和教育，旨在提高我们对无限电子海洋在冷却至接近绝对零度时集体运动的理解。这个“量子多体问题”之所以复杂，是因为有大量的电子相互影响，也是因为在如此低的温度下，日常经验所不熟悉的量子力学定律开始起作用。我们对描述所涉及的物理现象的理论的理解在描述各种材料的性质方面找到了重要的应用。量子多体系统可以显示的现象范围很广，而且还在不断被发现。电子状态的微小变化可以使它们的行为产生巨大的变化。在量子磁学中发现了一类重要的现象，其中包括对材料中自发发展的内部磁场模式的研究。在上个世纪，实验技术的进步导致了数百种具有不寻常磁性行为的材料的发现。将测量的磁性行为与形成材料的原子的性质联系起来是一个重要的挑战，无论是对于我们对自然的基本理解还是对于新型磁体在技术中的潜在应用。 计算机模拟已成为解决此类问题的有力工具。本项目的主要内容之一是开发和应用新的计算机算法，以解决量子磁学中尚未解决的问题。除了研究之外，本项目还将有助于培养和教育凝聚态物理和先进计算方法领域的本科生和研究生，为他们毕业后提供广泛的就业机会。PI还将访问肯塔基州大学以外的地方，访问肯塔基州的各个文科学院（包括中心学院和伯里亚学院），提供量子物理学的普及讲座，并与学生讨论研究生院的未来机会。暑期研究机会也将提供给学生在邻近的文科院校。PI将致力于通过在国家和国际场所组织会议和研讨会，建立核和粒子理论界与凝聚态界之间的合作和联系。技术概述该奖项支持强关联量子凝聚态物理领域的理论和计算研究和教育，结合大规模数值模拟和场论研究。数值研究将涉及新算法的开发，以研究强相关系统以及它们在一些感兴趣的问题中的应用。研究的主要课题包括：（1）非二分量子自旋模型中的自旋液相，（2）自旋模型中的量子自旋类冰涌现电动力学，（3）无序自旋系统中的量子临界性，（4）二维和三维中具有二次带接触的晶格费米子模型的模拟，并应用于双层石墨烯和烧绿石铱酸盐，（5）二维和三维中相互作用对狄拉克费米子的影响，并应用于各种强关联系统，（6）二维自旋模型的去限制临界性，（7）提高了对QMC的“符号问题”的认识，拓宽了符号问题的范畴;首要的主题是确定新的现象，基本上涉及强电子-电子相互作用，不能用微扰方法分析。除了研究，该项目将有助于凝聚态物理和先进计算方法领域的本科生和研究生的培训和教育，为他们毕业后开辟广泛的就业机会。PI还将访问肯塔基州大学以外的地方，访问肯塔基州的各个文科学院（包括中心学院和伯里亚学院），提供量子物理学的普及讲座，并与学生讨论研究生院的未来机会。暑期研究机会也将提供给学生在邻近的文科院校。PI将致力于通过在国家和国际场所组织会议和研讨会，在核和粒子理论界与凝聚态界之间建立合作和联系。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research and education aimed at improving our understanding of the collective motion of an infinite sea of electrons when they are cooled close to the absolute zero of temperature. The complexity of this "quantum many-body problem" arises both because there is a large number of electrons that influence each other and also because at such low temperatures the unfamiliar to everyday experience laws of quantum mechanics become operative. Our understanding of theories to describe the physical phenomena involved finds important applications in describing the properties of a wide range of materials.The range of phenomena that quantum many-body systems can display is wide and more are being constantly discovered. Small changes in the conditions of the electrons can produce dramatic changes in their behavior. An important class of phenomena where this is evident is found in quantum magnetism, which encompasses the study of patterns of internal magnetic fields that develop spontaneously in materials. In the last century, advances in experimental techniques have resulted in the discovery of hundreds of materials with unusual magnetic behavior. Linking the measured magnetic behavior to the nature of the atoms that form the materials is an important challenge, both for our fundamental understanding of nature and for potential applications of novel magnets in technology. Computer simulations have emerged as a powerful tool to solve such problems. A major component of this project will be the development and application of novel computer algorithms to tackle unsolved problems in quantum magnetism.In addition to research, the project will contribute to the training and education of undergraduate and graduate students in the fields of condensed matter physics and advanced computational methods, opening up a broad spectrum of career opportunities for them after graduation. The PI will also reach outside the University of Kentucky, by visiting various liberal arts colleges in the state of Kentucky (including Centre College and Berea College), giving popular-level lectures on quantum physics and leading discussions with students on future opportunities in graduate school. Summer research opportunities will also be offered to students at neighboring liberal arts colleges. The PI will work to forge collaborations and connections between the nuclear and particle theory community and the condensed matter community though the organization of conferences and symposia at national and international venues.TECHNICAL SUMMARYThis award supports theoretical and computational research and education in the field of strongly correlated quantum condensed matter physics, combining large-scale numerical simulations and field theoretic studies. The numerical research will involve both the development of new algorithms to study strongly correlated systems as well as their application to a number of problems of interest. Some of the major topics to be studied include:(1) spin-liquid phases in non-bipartite quantum spin models,(2) quantum-spin-ice-like emergent electrodynamics in spin models,(3) quantum criticality in spin systems with disorder,(4) simulations of lattice fermion models with quadratic band touching in two and three dimensions with applications to bilayer graphene and the pyrochlore iridates,(5) the effect of interactions on Dirac fermions in two and three dimensions, with applications to various strongly correlated systems,(6) deconfined criticality of two-dimensional spin models,(7) improvement of our understanding of the "sign problem" of QMC and broadening the class of sign-problem-free models.The overarching theme is to identify new phenomena that essentially involve strong electron-electron interactions and which cannot be analyzed by perturbative methods. In addition to research, the project will contribute to the training and education of undergraduate and graduate students in the fields of condensed matter physics and advanced computational methods, opening up a broad spectrum of career opportunities for them after graduation. The PI will also reach outside the University of Kentucky, by visiting various liberal arts colleges in the state of Kentucky (including Centre College and Berea College), giving popular-level lectures on quantum physics and leading discussions with students on future opportunities in graduate school. Summer research opportunities will also be offered to students at neighboring liberal arts colleges. The PI will work to forge collaborations and connections between the nuclear and particle theory community and the condensed matter community though the organization of conferences and symposia at national and international venues.