CAREER: Theoretical Investigation of Interacting Topological States of Matter

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TECHNICAL SUMMARYThis CAREER award supports theoretical research and education to systematically investigate interacting topological states of matter. In recent years, a systematical understanding has been obtained for non-interacting topological states of matter in generic symmetry classes. However, interacting topological states of matter are much less understood, and novel physical phenomena such as quantum number fractionalization are expected to occur, as has been learned from fractional quantum Hall states. The PI plans to systematically characterize interacting topological states of matter in different dimensions and symmetry classes, through a combination of three approaches:i) Construction and characterization of many-body ground state wavefunctions. The many-body ground state wavefunction provides a complete description of the ground state properties. The PI plans to generalize the wavefunction approach to fractional quantum Hall states, and construct ground state wavefunctions and corresponding model Hamiltonians of two-dimensional and three-dimensional topological states. ii) Topological field theory description. Topological field theory describes topological states by their observable physical properties. The PI aims to develop new topological field theories for topological states especially for topological superconductors. iii) Quantum entanglement properties of topological states and their relation to dynamical properties of the system. The PI will study the entanglement spectrum of topological states and also develop new characteristics of quantum entanglement properties.The proposed research will be integrated with education of graduate and undergraduate students. This project will provide graduate students with a unique research experience involving both solid training in theoretical condensed matter physics and a broad view of many related fields. The PI will make sustained efforts to introduce the proposed research to undergraduate students through lectures, classes and research projects. The PI has been active in organizing tutorials and workshops, writing review articles and pedagogical articles to benefit both junior and senior members of the community, and to introduce research results on topological states of matter to a broader audience. The PI plans to prepare public lectures on topological physics to disseminate the research results of this project and to attract broader interest in this subject beyond the physics community.NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to systematically investigate topological states of matter involving electrons that interact strongly with each other. The first topological states of matter discovered are the quantum Hall effects which arise in electrons trapped in two dimensional sheets that are exposed to a large perpendicular magnetic field. A new topological state is the topological insulator. Like ordinary insulators, for example rubber, topological insulators do not conduct electricity through the interior of the material. Unlike ordinary insulators, topological insulators are able to conduct electricity on their edges or boundaries through the formation of a new state of matter. Among the known topological insulators are compounds made of the elements bismuth and selenium, and bismuth and tellurium.The PI aims to study the effect of the correlated motion of electrons that arise from strong interactions between electrons in topological states of matter. The current understanding of topological insulators largely neglects correlations. The PI aims to systematically characterize interacting topological states from several complimentary aspects. Correlations may lead to the discovery of new states of matter with properties that may be exploited for device applications. The PI will study the properties and the quanutm mechanical structure of these states. The PI will propose experimentally observable signatures of new topological states that qualitatively from familiar well understood states of matter. The proposed research will be integrated with education of graduate and undergraduate students. The PI will make sustained efforts to introduce the proposed research to undergraduate students through lectures, classes and research projects. The PI has been active in organizing tutorials and workshops, communicating science to benefit both junior and senior members of the community, introducing the research results on topological states of matter to a broader audience. The PI will prepare public lectures on topological physics to disseminate the research results of this project and to attract broader interest in this subject beyond the physics community.