Novel phases of electronic insulators and quantum Hall systems

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NONTECHNICAL SUMMARYThis award supports theoretical research and education on the physics of new kinds of quantum phenomena in materials. The electronic properties of most solids are understood within a quantum mechanical description of a large number of interacting electrons that are moving in the background of charged atom cores that form the bulk of the solid. An important modern realization is that due to quantum mechanics, the properties of spatially distant electrons in the solid can be inextricably tied together, a phenomenon called entanglement. Quantum mechanical entanglement plays a role in determining macroscopic properties of the solid. A striking and paradigmatic example occurs when the motion of electrons is restricted to two dimensions and is subjected to a strong perpendicular magnetic field.The PI will develop new concepts and methods to deal with such electronic states and their identification in experiments. He will also develop a deeper understanding of the interplay between symmetry and entanglement, which are two of the central pillars of modern quantum physics. Historically, such fundamental research on electronic materials has generated many of the concepts that underlie modern electronic technology. The proposed research will contribute to the continuum of scientific and technological knowledge enabling future technology that harvests quantum entanglement in fundamental ways.In addition to research, the award supports the training of graduate students in modern concepts and methods in condensed-matter physics. Undergraduates will be involved in the research when possible. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and the associated experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists. TECHNICAL SUMMARYThis award supports theoretical research and education on the physics of novel quantum states of electronic insulators and quantum Hall systems. Specific phases of interest are liquids of composite fermions in quantum Hall systems, quantum spin liquids in insulating magnets, and strongly correlated relatives of topological insulators. There has been a remarkable convergence of these three seemingly different topics in the last two years. The project will develop these connections further and exploit them to further our understanding of each topic. Specific questions that will be pursued are: i) a microscopic lowest-Landau-level theory of the metallic particle-hole-symmetric half-filled Landau level, ii) a theoretical description of current experiments on quantum spin liquid states, iii) theory and realization of strong correlation effects in topological insulators.Project (i) is fundamental to the theory of the quantum Hall effect and seeks to provide a microscopic foundation to recent developments on a long-wavelength effective theory for the metallic state in the half-filled Landau level. Project (ii) will seek to develop the theory of quantum spin liquids in contact with many ongoing experiments on Mott insulators that find evidence for various kinds of quantum spin-liquid phases. Project (iii) will study the interplay of strong correlation effects and topological insulator phenomena, two cornerstones of modern work on quantum materials. In addition to research, the award supports the training of graduate students in modern concepts and methods in condensed-matter physics. Undergraduates will be involved in the research when possible. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and the associated experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists.