This award supports theoretical research and education in condensed matter physics with an emphasis on a deeper understanding of the notion of order in states of matter. A comprehensive theory for symmetry breaking order has been developed, based on the concept of an order parameter, Ginzburg-Landau theory, and group theory. Such a theory forms a corner stone in the foundation of condensed matter theory. The PI has proposed the concepts of topological order and quantum order that are outside the standard Landau-Ginzburg theory of phase transitions. In this research project, the PI plans to develop a more complete theory of topological/quantum order. Specifically, the PI plans to apply the string-net mean-field theory to realistic quantum spin systems to identify materials that may contain non-trivial topological/quantum order. Strong fluctuations of ends of string and their close tie to the continuous transition between topological states will be studied. This may lead to a general theory for topological phase transitions, where the projective symmetry associated with the ends of string may play a key role. In particular, Topological phase transitions may lead to non-Abelian FQH states in double-layer systems which can realize universal quantum computations. The emergent gauge theory in string condensed states may also be the key to understand the novel properties of high temperature superconductors. The PI plans to use a newly developed spinon-dopon theory to gain a more quantitative understanding of high temperature superconductors. A theme of the research is to build a closer connection between the general theory of topological/quantum order and experimental observations, such as those in high temperature superconductors, that appear to defy a conventional explanation. This research may also lead to predictions of new materials and new phenomena.
NON-TECHNICAL SUMMARY: This award supports research and education in fundamental theoretical condensed matter physics. The notion of order is an important cornerstone in the foundation of our understanding of the world around us. When liquid with atoms solidifies, the atoms may organize themselves in a periodic array to form a crystal lattice. This is an example of an ordered state of matter; there are many other diverse examples, some more exotic and subtle, in the world around us that can be organized and described by standard theory of phase transitions. The discovery of new materials, like the high temperature superconductors, and states of matter like the quantum Hall phases that arise when electrons are confined to two dimensions in a high magnetic field, has led to questions about fundamental nature of order and whether the concept is more general than our current notion. The PI proposes a specific new kind of order that is not contained in the standard theory of phase transitions, but yet would have significant consequences on how we understand puzzling experiments in various exotic materials. This award supports research that aims to develop a theory of transformations involving these new ordered states and to discover the validity and consequences of this idea. Predictions of new phenomena and possible new states of matter may result from this work; the potential impact on future technologies and other disciplines cannot be estimated. This project also involves students and will help train the next generation of condensed matter theorists.
