Topological Phases, Supersymmetry, and Disordered Systems

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TECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences provide funds for this award. It supports theoretical research and education in the area of low-temperature phenomena in both classical and quantum condensed matter systems. Specifically, these include the quantum Hall regime of an electron gas that occurs in a two-dimensional electron gas in a high magnetic field, with the goal of understanding the non-Abelian topological phases of matter in this and other systems in greater depth. There is now a large experimental and theoretical effort aimed at using such systems for topological quantum computation. Another focus is disordered systems, including non-interacting fermions in two dimensions as in the integer quantum Hall effect, with the use of algebraic techniques applied to lattice models and conformal field theory of critical points. Disordered systems arising from optimization and their connections with statistical physics problems such as classical spin glasses will also be addressed. While the research will concentrate on deepening the understanding of fundamental properties, applications to experiments will be made wherever possible.NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences provide funds for this award. It supports theoretical research and education at the interface of condensed matter physics and mathematics. The ability of electrons sandwiched between semiconductors into thin layers in a high magnetic field to conduct electricity is fixed in discrete amounts. Theory predicts that these remarkable quantum Hall effects signal that electrons in two dimensions in a magnetic field can organize themselves into subtle new states of matter. This award supports research that further explores the nature of these states. Since their prediction, it has been realized that the unusual properties of these new states of matter can form the basis for new kinds of computers, so called topological quantum computers. The operation of these computers would be particularly resistant to noise from the environment that normally spoils essential properties of quantum mechanical states. Learning more about exotic quantum mechanical systems and materials and revealing their technological value requires highly sophisticated mathematics and the creativity behind theoretical physics. The ideas and fundamental knowledge generated by endeavors such as these contribute to future technologies not yet envisioned, but contribute to the foundation of this Nation's future success in global economic competition.