Applications of Field Theory to Condensed Matter Physics

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NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems whose behavior is governed by strong effects of quantum mechanics and strong interactions between their constituent electrons. Such understanding could lead to the prediction of new states of matter with novel properties as well as to the discovery of new materials with potentially useful applications. The PI and his collaborators have predicted the existence of strongly interacting quantum states of matter, named intertwined orders, in which electrons organize themselves in complex patterns. Intertwined orders describe physical systems in which, due to the strong interactions between the constituent electrons, different and seemingly competing types of organization coexist and emerge together with nearly equal strength. Superconductors are a relevant example. These are materials in which, at sufficiently low temperatures, electrons enter a cooperative quantum mechanical state that enables them to conduct electricity without any resistance. High-temperature superconductors are a particularly interesting species because they exhibit superconductivity at much higher temperatures than many other known classes of superconductors. The PI's proposed state of matter may help explain how this is possible, and how materials that exhibit superconductivity at room temperature might be discovered. This could lead to virtually lossless transmission of electric power and other energy-related applications. The other focus of the research concerns the understanding of new states of matter, called topological phases, which are essentially immune to the usually destructive effects that disorder and other defects have on material properties. Topological phases are predicted to have unusual properties that could enable computation based on the laws of quantum mechanics. A quantum computer could solve certain problems much faster than any currently existing computer.  The research involves cutting-edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices. Research and education will be further integrated through the development of advanced curricular materials.TECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems involving many strongly coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics. The electrons in such strongly correlated systems organize spontaneously in electronic liquid-crystal phases and in topological phases. An unavoidable feature of these phases is that they naturally describe intertwined orders. The main focus of the project is on the theory of intertwined orders in strongly correlated systems, and on topological phases of matter. Both lines of research require the development of new theoretical insights and the use of methods and ideas from quantum field theory. The projects include studies of the emergence of pair-density-wave superconducting states in microscopic models, both in a quasi-one-dimensional setting and in ladder systems, developing an effective field theory of pair-density-wave and charge 4e superconducting states, and uncovering the mechanism connecting electronic nematic order and superconductivity. The PI's work on topological phases of matter aims to establish a relation between electronic nematic order and paired quantum Hall states (a form of intertwined orders), and to develop the lattice Chern-Simons gauge theory of frustrated quantum antiferromagnets, with applications to the theory of fractionalized Chern insulators. An important new project aims at finding a relation between the theory of quantum critical loops that the PI developed earlier and the recently conjectured quantum dualities for Dirac systems.The research involves cutting-edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices. Research and education will be further integrated through the development of advanced curricular materials.