Applications of Field Theory to Condensed Matter Physics

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TECHNICAL SUMMARY:This award supports theoretical research on new states of 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. This is a frontier area of research in which the understanding of some of the most fundamental problems in physics is achieved by experiments done at the cutting edge of technology. Electronic liquid crystal phases are states of matter in which strongly correlated electrons organize themselves in inhomogeneous and anisotropic patterns. They are closely related to mechanisms of high temperature superconductivity, a fundamental problem in physics which already has had a strong impact in technology. 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 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. Such an approach enables the project to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics.NON-TECHNICAL SUMMARY:This award supports theoretical research that aims 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. One focus of the research is on exciting states of matter that are theoretically predicted to exist in a sheet of electrons in a strong magnetic field perpendicular to the sheet. These conditions can be realized in special semiconductor structures. The states of matter, called topological states, have yet to be confirmed experimentally. A challenge of the research is to propose experiments that can unambiguously detect them and to understand their properties. Understanding how these states of matter can be controlled may lead to a new kind of computer that depends on the purposeful manipulation of quantum mechanical states for its operation and would be able to carry out certain calculations much more rapidly than current computers. Another focus of the research is to further understand new quantum mechanical states of electrons that have been proposed by the PI and collaborators. The 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. Recent experiments support the existence these states which are proposed to play an important role in understanding the high temperature superconductors.The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientist. It also opens new possibilities for future technologies.