Novel Phases of Quantum Matter in Numerical Simulations, Field Theory and Materials

NONTECHNICAL SUMMARYThis award supports theoretical and computational research that covers a selection of topics at the forefront of condensed matter theory and materials science with a focus on magnetism and systems in which electrons interact strongly with each other. Magnetism is a striking example of a phenomenon which arises in crystal materials entirely due to the subtle laws of quantum mechanics. Even though magnetism has been observed and studied since ancient times, modern experimental studies have found time and again this phenomenon to be surprisingly diverse and rich, inspiring a whole new range of intellectual problems for theoretical physicists. For example, it is now well known that one can destroy magnetism by heating any magnetic material above a certain temperature, but studies during the last several decades have indicated that it is also possible to destroy magnetism at the absolute zero of temperature. The mechanisms by which this destruction occurs are subtle, and their fundamental origin is being intensely studied and debated. This research project will contribute to this important scientific endeavor by developing new computational algorithms to study special models of magnetism that can be simulated on a supercomputer and providing an unusual window to this fascinating phenomenon. In addition to this research, the PI will study how magnetism and other quantum mechanical effects arising from strong electron-electron interactions can be created and controlled in specific materials in a laboratory, such as in few layers of carbon atoms stacked on top of each other. A major part of this project involves the training of graduate and undergraduate students in materials science and computational algorithms. The PI will continue to deliver advanced lectures for graduate students and researchers at various institutions and training schools, and make his lecture notes available on his website. The PI will develop his outreach activities outside the University of Kentucky, by visiting four-year colleges (Morehead State University, Centre College, and Berea College) in the state of Kentucky, where he will give pop-science level lectures on quantum physics and lead discussions with students on future opportunities in graduate school. Finally, the PI will continue to organize international conferences that bring together condensed matter and high energy physics researchers that use similar theoretical and computational tools in their respective research areas.TECHNICAL SUMMARYThis award supports theoretical and computational research that covers a selection of topics at the forefront of condensed matter theory and materials science with a focus on quantum many body effects, from the study of basic models of many body physics with numerical and field theoretic methods to the analysis of experimental data. Specific projects include quantum phase transitions of two dimensional spin models with S>1/2, quantum criticality of Dirac fermions, algorithmic development for unbiased studies of lattice models of quantum spins and correlated fermions, effects of strong correlations in multi-layer graphene systems and the study of frustrated magnetism and heavy fermion behavior in the family of R2T2X materials. The overarching theme is to identify new phenomena both theoretically and in experiment that involve strong electron-electron interactions that cannot be analyzed by perturbative methods.A major part of this project involves the training of graduate and undergraduate students in materials science and computational algorithms. The PI will continue to deliver advanced lectures for graduate students and researchers at various institutions and training schools, and make his lecture notes available on his website. The PI will develop his outreach activities outside the University of Kentucky, by visiting four-year colleges (Morehead State University, Centre College, and Berea College) in the state of Kentucky, where he will give pop-science level lectures on quantum physics and lead discussions with students on future opportunities in graduate school. Finally, the PI will work to forge collaborations and connections between the lattice gauge theory and condensed matter communities, through organization of conferences and symposia, at national and international venues.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.