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

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到接近绝对零度时的集体运动的理解。这种“量子多体问题”之所以复杂，一方面是因为存在大量相互影响的电子，另一方面是因为在如此低的温度下，日常经验中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有着重要的应用。量子多体系统可以显示的现象范围很广，而且还在不断地被发现。电子环境的微小变化可以引起它们行为的巨大变化。量子磁学是一类重要的现象，它包括对材料中自发形成的内部磁场模式的研究。在上个世纪，实验技术的进步导致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，无论是对我们对自然的基本理解还是对新磁铁在技术上的潜在应用。计算机模拟已经成为解决这类问题的有力工具。该项目的一个主要组成部分将是开发和应用新的计算机算法来解决量子磁学中尚未解决的问题。除了研究之外，该项目还将为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做出贡献，为他们毕业后开辟广阔的职业机会。PI还将触及肯塔基大学以外的地区，访问肯塔基州的各种文理学院（包括中央学院和伯里亚学院），举办量子物理学的通俗讲座，并与学生讨论未来在研究生院的机会。邻近文理学院的学生也将获得暑期研究机会。PI将通过在国内和国际场合组织会议和专题讨论会，努力在核与粒子理论界和凝聚态物质界之间建立合作和联系。该奖项支持强相关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现场理论研究。数值研究将涉及研究强相关系统的新算法的发展，以及它们在一些感兴趣的问题上的应用。一些主要的研究课题包括：(1)非二部量子自旋模型中的自旋液相，(2)自旋模型中的量子自旋冰状突现电动力学，(3)无序自旋系统中的量子临界，(4)二维和三维二次带接触晶格费米子模型的模拟及其在双层石墨烯和焦绿石铱酸盐中的应用，(5)相互作用对二维和三维狄拉克费米子的影响，通过对各种强相关系统的应用，(6)定义了二维自旋模型的临界性，(7)提高了我们对QMC“符号问题”的理解，拓宽了无符号问题模型的类别。总体主题是确定本质上涉及强电子-电子相互作用的新现象，这些现象不能用微扰方法分析。除了研究之外，该项目还将为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做出贡献，为他们毕业后开辟广阔的职业机会。PI还将触及肯塔基大学以外的地区，访问肯塔基州的各种文理学院（包括中央学院和伯里亚学院），举办量子物理学的通俗讲座，并与学生讨论未来在研究生院的机会。邻近文理学院的学生也将获得暑期研究机会。PI将通过在国内和国际场合组织会议和专题讨论会，努力在核与粒子理论界和凝聚态物质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.