Frustrated Quantum Magnetism in Insulators and Metals

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TECHNICAL SUMMARY:This award supports theoretical research and education on the quantum theory of localized magnetic moments in diverse circumstances in solids. Specific topics of interest are the quantum phases and phase transitions of interacting localized magnetic moments in both insulating and metallic materials. This area has been invigorated by the discovery of a number of new materials with unusual properties that challenge conventional paradigms of condensed matter physics. The emphasis of this proposal will be on general development of theoretical concepts in the context of either experiments on specific materials or numerical work on specific microscopic models.The research aims to advance understanding of: (i) quantum phase transitions in triangular antiferromagnets, (ii) spin nematic order and disorder, (iii) gapless quantum spin liquids, (iv) deconfined quantum criticality in three dimensions, and (v) the interplay between magnetism and Kondo effect in heavy fermion metals. The former three are motivated by experiments and numerical calculations on a number of materials and models. The PI aims to discover key insights that will be useful in interpreting the results from experiments, and that will help suggest new ones that will clarify the nature of these new states of matter and the transformations among them. Projects (iv) and (v) are part of a long term research effort to exploit intuition from the theory of insulating magnets toward building a theory of non-Fermi liquid heavy electron critical points. To that end the PI will explore the possibility of unconventional quantum criticality in three dimensional insulators in project (iv). In project (v) he will attempt to identify configurations in the heavy Fermi liquid which might drive the transition to magnetism.The PI will involve undergraduates in the research, when possible, through theUndergraduate Research Opportunities Program at MIT. The PI plans to write a book that will introduce some of the exciting modern developments on fractional quantum numbers in condensed matter physics to a broad physics audience.NON-TECHNICAL SUMMARY:This award supports theoretical research and education that aims to discover new magnetic states of matter and to understand exotic transformations that can occur among them that lie outside the standard theory of phase transitions. This research is motivated and stimulated by the discovery of new materials with unusual properties that challenge conventional paradigms of condensed matter physics. The emphasis of this research will be on developing theoretical concepts in the context of laboratory and computer experiments on materials and models.This is fundamental research that contributes to the intellectual foundations of our understanding of materials and new states of matter that exhibit properties and exotic phenomena that lie outside our current understanding. This is an intellectual pursuit in its own right no less fascinating than the study of the universe, but it may also lead to the discovery of new phenomena and to new device technologies.