This award supports theoretical research and education to develop advanced theoretical tools to tackle problems in areas that include quantum entanglement, topological insulators, the plateau transition in the integer quantum Hall effect, and quantum critical phenomena. Many of the most interesting, or newly emerging phenomena in condensed matter physics cannot be understood in terms of existing paradigms and techniques, and the development of new methods or approaches for their description is often needed. Materials of particular interest include those where electronic behavior is dominated by strong interactions and strong disorder, and those exhibiting topological features. The understanding of such systems is often very challenging due to the limited number of theoretical tools available for their investigation. The focus of the work supported under this award is the development and the application of novel methods and techniques in condensed matter theory, a process that also benefits from recent advances in the mathematical sciences. The PI aims to develop theoretical tools in the context of the study of quantum entanglement and quantum information, topological states of matter and topological insulators, and localization transitions in disordered electronic systems. The methods planned to be employed range from topology, to conformal field theory, the Schramm-Loewner Evolution and the functional renormalization group.
NONTECHNICAL SUMMARY This award supports theoretical research and education aimed at the discovery and study of novel phases of matter. The latter often exhibit completely new phenomena and may possess highly unusual properties that can hold promise to form the basis of future technologies. One recent example is the discovery of topological insulators, which are insulators in the bulk but conductors at the surface. Another example is a notion called non-Abelian statistics, a possible quantum property of electronic materials which has been proposed to form the physical underpinnings of what is known as a fault-tolerant quantum computer whose realization would mark the dawn of an entirely new era of computation. As new phenomena appear in condensed matter physics, the development of novel methods or approaches for their description is often called for. This typically occurs in electronic systems dominated by strong interactions, or by the presence of strong disorder arising from omnipresent sample impurities. The focus of this project is the development and the application of new theoretical tools in condensed matter theory, some of which benefit from recent advances in the mathematical sciences. Today's newly developed methods will belong to the standard repertoire of tools available to the next generation of researchers. This research activity aims to advance fundamental science at the frontiers of condensed matter theory, with the potential to contribute to the development of future technologies. It will also contribute to the training and mentoring of graduate students and postdoctoral researchers interacting with the PI on this project. This activity will thus contribute to the education of the next generation of condensed matter theorists.
