Applications of Field Theory to Condensed Matter Physics

点击翻译按钮获取中文摘要

NON-TECHNICAL SUMMARYThis award supports theoretical research aimed at understanding condensed matter systems involving many coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics, in particular strong interactions between electrons. Such understanding could lead to the prediction of new states of matter with novel properties as well as new materials with potentially useful applications. A particular state of strongly interacting electrons originally predicted by the PI and his collaborators emerges in the so-called electronic liquid crystal phase, which is a quantum mechanical analogue of molecules found in liquid crystal displays, sharing properties of both a solid and a liquid. The PI will further investigate whether such phases can explain the peculiar properties of materials known as high temperature superconductors. At sufficiently low temperatures, electrons in superconductors enter a cooperative quantum mechanical state that enables them to conduct electricity without any resistance. High temperature superconductors are interesting 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 temperatures 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 experiments seeking new states of matter, in particular the so-called topological states, which are predicted to have unusual properties that would enable computation based on the laws of quantum mechanics. Such a computer could solve certain problems much faster than any currently existing computer. The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. Research and education will be further integrated through the development of advanced curricular materials. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices.TECHNICAL SUMMARYThis project provides support for research into the theory of 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 topological phases. An unavoidable feature of these phases is that they naturally describe intertwined orders. The main projects focus 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 and transformative theoretical insights and the use of methods and ideas of quantum field theory. The particular topics that will be investigated include the relation between electronic liquid crystal phases and high temperature superconductivity, quantum coherence and interference phenomena in quantum Hall systems, quantum entanglement and topological quantum computing.The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. Research and education will be further integrated through the development of advanced curricular materials. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices.