Applications of Field Theory to Condensed Matter Physics

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TECHNICAL SUMMARYThis award supports theoretical research and education on the theory of condensed matter. The objective is to understand 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. The PI will investigate electronic liquid crystal and topological phases. Electronic liquid crystal phases are states of matter in which strongly correlated electrons organize themselves in inhomogeneous and anisotropic patterns. Topological phases are quantum fluid states of matter that do not have an order parameter, and therefore do not break any symmetry, but possess a kind of hidden quantum order in which the ground state degeneracy is determined by the topology of the space in which they live. The quantum states of a topological fluid are strongly entangled, a property that can be used to devise a topological quantum computer, a frontier problem in physics and mathematics having great potential impact on technology. Related 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 nature of the problems that the PI studies requires the use of the methods and ideas of quantum field theory. These are the best tools with which to attack problems involving the statistical and quantum physics of strongly interacting systems. This approach enables the PI to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics.This award supports the continued training of talented theoretical scientists. The PI has a strong record of training outstanding scientists, including many Hispanic and women scientists, and in integrating research and education through the development of advanced curricular materials. NONTECHNICAL SUMMARYThis award supports theoretical research with an aim to predict new states of matter and to develop fundamental understanding of their novel properties. The emphasis of the research will be on states of matter that emerge from electrons that interact strongly with each other and are confined to two dimensions. The PI will further investigate states of electrons in solids originally predicted by the PI and collaborators. These states are quantum mechanical analogs to the phases of molecules found in liquid crystal displays which share properties of both a solid and a liquid. Electrons in these states organize themselves in a way so that they can flow like a liquid but exhibit patterns of orientation and symmetry that are reminiscent of the way atoms are arranged in a solid. The PI will pursue whether these states can explain the unusual form of superconductivity in materials known as high temperature superconductors. At sufficiently low temperatures, the electrons in superconductors enter a cooperative quantum mechanical state that enables them to conduct electricity without loss, along with other interesting properties. The high temperature superconductors are interesting because they exhibit superconductivity at higher temperatures than any other known class of superconductors. The PI's proposed state of matter may help explain how this is possible and how superconductors might be discovered that exhibit superconductivity at room temperature. 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 and pursuing new questions that they raise. The new states of matter are predicted to exist in a sheet of electrons in a strong magnetic field perpendicular to the sheet, conditions that can be realized in specially fabricated semiconductor materials. The states of matter, called topological states, 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. Drawing in part from advances in the field of quantum information theory and the findings of recent experiments, the PI will advance the theory of these new states, seeking to come closer to the realization of how to make a topological quantum computer.The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientist. Research and education will be further integrated through the development of advanced curricular materials. It also opens new possibilities for future technologies.