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

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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.