Disordered Systems, Supersymmetry, and Topological Phases

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TECHNICAL SUMMARY:This award supports theoretical research and education in low temperature phenomena in both classical and quantum condensed matter systems. Specifically, these include the quantum Hall regime 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. Included in the investigations is the possibility of 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 spin glasses will also be addressed.NON-TECHNICAL SUMMARY:This award supports theoretical research and education in theoretical condensed matter physics at the interface with mathematics. With the discovery that the electric conductivity of thin materials sandwiched into thin layers in a magnetic field was fixed to certain discrete amounts, that was the beginning of research on the quantum hall effect. The electrons confined to a thin layer exhibit unusual structures because of the quantum mechanical laws that govern motion for small particles at small distances. This has proven to be an extraordinarily rich topics because of the many usual behaviors, some reflecting new states of matter. Research in this grant involves the specific topics of electrons confined to layers and includes some investigation of new states of matter associated with the fractional quantum hall effect. Since the prediction of these new states of matter, it has also become possible that the unusual properties of some of them could be 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 these exotic quantum systems so that they may be of potential 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.