This grant provides support for research into the theory of condensed matter. The objective is to understand condensed matter systems involving strongly coupled degrees of freedom, and in particular the phase diagram and quantum critical behavior of topological phases and electronic liquid crystal phases. Topological phases are states of matter that do not have an order parameter, and are therefore not the product of spontaneous symmetry breaking, but posses a kind of "quantum order" in which the ground state degeneracy is determined by the topology of the space in which they live. Electronic liquid crystal phases are states of matter in which strongly correlated electronic organize themselves in inhomogeneous and anisotropic patterns, and are closely related with mechanisms of high temperature superconductivity. Related topics that will be investigated include quantum coherence and interference phenomena in quantum Hall systems and strongly coupled junctions, and the relation between electronic liquid crystal phases and high temperature superconductivity.
The nature of the problems to be studied requires the methods and ideas of quantum field theory. This is the best tool with which to attack problems involving the statistical and quantum physics of strongly interacting systems. It enables this research to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems and high energy physics.
Intellectual Merit: The research addresses a range of important and difficult problems in currently fertile, and therefore very active, areas of fundamental physics.
Broader Impact: The grant makes possible the continued training of talented researchers. The principal investigator has an excellent record training students and postdoctoral associates, and his work with Hispanic and female scientists is particularly noted. %%% This grant supports research that is at the core of modern condensed matter physics. In particular, the principal investigator will apply advanced theoretical techniques to the study of exotic phases of electrons that interact strongly with each other. Besides the fundamental interest in these phases and associated phenomena, e.g., high temperature superconductivity, these studies may lead to the discovery of new materials and devices. The research provides an excellent training ground for students.
