Field Theoretical Methods in Strongly Interacting and Strongly Disordered Condensed Matter Physics

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

TECHNICAL SUMMARY: This award supports theoretical research and education under the umbrella of the NSF-wide Mathematical Sciences Priority Area. This project lies at the interface of theoretical condensed matter physics and mathematics. Many interesting phenomena observed in the condensed matter physics laboratory are dominated by strong interactions or strong disorder. The understanding of such systems is typically very challenging, due to the limited number of theoretical tools available for their description, standard paradigms including for example Fermi-Liquid or other independent particle-type approaches are often not adequate to capture the The focus of the work supported under this award is the application and the Development of novel theoretical methods aimed at treating such strong coupling problems. The focus of the research includes Non-Fermi-Liquid behavior in Quantum Impurity Problems dominated by strong interactions, localization Transitions in disordered electronic systems, and systems dominated by the simultaneous effects of disorder and interactions. The PI will use methods ranging from conformal field theory, to the functional renormalization group, and the emerging field of the Stochastic Loewner Evolution. NON-TECHNICAL SUMMARY: This award supports theoretical research and education under the umbrella of The NSF-wide Mathematical Sciences Priority Area. This project lies at the Interface of theoretical condensed matter physics and mathematics. This research focuses on problems at the frontiers of condensed matter theory that involve materials or nanosystems with unusual properties. These often arise as a consequence of strong interactions among electrons. Disorder, where the positions of the atoms deviate significantly from highly ordered arrangements, may also play an important role. Understanding the effects of these two factors working in concert represents a formidable theoretical challenge. The PI will, develop new theoretical tools, some that benefit from recent advances in the mathematical sciences, to advance research on the combined effects of strong interaction and disorder in materials. This research aims to advance fundamental science and it interesting and important in its own right. It may also contribute to the discovery of new phenomena and contribute to our understanding of complex materials that hold promise for future technological applications. This research activity will contribute to the education of the next generation of condensed matter theorist.