CAREER: Geometry and Interference in Strongly Correlated Systems

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This CAREER award is co-funded by the Materials Theory program of the Division of Materials Research and the Topology program of the Division of Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. This CAREER award supports theoretical research and education involving the application of topological methods and new theoretical methods to outstanding problems in condensed matter theory. The research will establish a basis for further studies of the physics of strongly correlated and disordered systems. Research thrusts include: (i) calculating the probability of phase slips in superconducting wires with applications to existing experiments, (ii) developing an effective low energy description in the presence of singular configurations, (iii) applying topological analysis and instanton calculus to the Coulomb blockade problem, (iv) developing a hydrodynamic approach as a non-linear bosonization to calculate the asymptotic behavior of correlation functions. In contrast to the symmetry analysis broadly used in condensed matter theory, topological analysis has not yet been widely accepted by the condensed matter community. This type of analysis has the potential to solve or to help solve many open problems. The proposed research will promote the use of topological methods in condensed matter theory and will strengthen connections with quantum field theory and mathematical physics. Some of the problems considered are deeply rooted in modern mathematics. Pursuing topological studies in condensed matter should turn out mutually beneficial for both condensed matter theory and mathematical physics.The educational component involves several activities that will be integrated with the research: (i) A review and lectures on topological methods in condensed matter physics will fill an important gap in graduate student (and more generally, condensed matter physics) education. These methods play an increasingly important role in modern physics. Creation of a new course on the use of topological methods with supporting materials on the Internet will reach a broader segment of the physics community and students. (ii) A new graduate course on Quantum magnetism will be developed to enhance graduate education and to bring together students from different research groups. (iii) Student symposia will be organized which, together with a strategy for attracting visitors to stay for longer times, will enhance education of graduate and undergraduate students from different research groups and will facilitate their active participation in research at earlier stages of their careers. (iv) A 'minimal set' of problems will be created for every mandatory graduate course to establish a common core for the physics department. It will be available online and may provide a resource for students and teaching faculty outside of the department.%%%This CAREER award is co-funded by the Materials Theory program of the Division of Materials Research and the Topology program of the Division of Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. This CAREER award supports theoretical research and education involving the application of advanced mathematical methods based on geometry and topology to outstanding problems in condensed matter theory. The PI will combine these methods with other advanced theoretical techniques and focus on a set of problems that seem ripe for advance from this viewpoint. Work on these problems will lay a foundation to attack the notoriously difficult and important problem of the nature of electronic states that arise from strong electron-electron interactions and disorder.In contrast to the symmetry analysis broadly used in condensed matter theory, topological analysis has not yet been widely accepted by the condensed matter community. This type of analysis has the potential to solve or to help solve many open problems. The proposed research will promote the use of topological methods in condensed matter theory and will strengthen the connections with quantum field theory and mathematical physics. Some of the problems considered are deeply rooted in modern mathematics. Pursuing topological studies in condensed matter should turn out mutually beneficial for both condensed matter theory and mathematical physics.The educational component involves several activities that will be integrated with the research: (i) A review and lectures on topological methods in condensed matter physics will fill an important gap in graduate student (and more generally, condensed matter physics) education. These methods play an increasingly important role in modern physics. Creation of a new course on the use of topological methods with supporting materials on the Internet will reach a broader segment of the physics community and students. (ii) A new graduate course on Quantum magnetism will be developed to enhance graduate education and to bring together students from different research groups. (iii) Student symposia will be organized which, together with a strategy for attracting visitors to stay for longer times, will enhance education of graduate and undergraduate students from different research groups and will facilitate their active participation in research at earlier stages of their careers. (iv) A 'minimal set' of problems will be created for every mandatory graduate course to establish a common core for the physics department. It will be available online and may provide a resource for students and teaching faculty outside of the department.***