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

NONTECHNICAL SUMMARY This 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 SUMMARY This 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.