Analytical and numerical studies of gapless fractionalized phases and topological phases and their transformations

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NON-TECHNICAL SUMMARY:This award supports theoretical research and education on how electrons in solid materials organize themselves as a result of the interactions among them. The way the electrons organize corresponds to new quantum mechanical states of matter. Because of the interactions among the particles, the quantum mechanical state of electrons can appear to be composed of new kinds of particles with properties that may differ dramatically from the properties of the constituent electrons or atoms. The PI will study two archetypal examples: i) instances where the microscopic particles interlock in such a way that it appears as if the entire system was comprised of particles with properties that are fractions of the original constituent electrons or atoms, e.g. even though electrons are indivisible the system of electrons behaves as if it were comprised of particles having one-third of an electron's charge, and ii) instances where the microscopic particles form an unusual soup where the system behaves as if comprised of particles that have no mass, which consequently can transport their exotic properties over long distances. Similar states of matter can also occur in systems of very cold atoms trapped in a lattice formed by laser beams organize themselves as a result of the interactions among them.The quantum mechanical states in the first example underlie ideas of specific proposals for a new kind of computer that manipulates quantum mechanical states to do computation. The quantum mechanical states in the second example may hold insights into understanding many technologically important materials, most notably high-temperature superconductors. The electrons in superconductors self-organize into a quantum mechanical state that can carry electric current without dissipation. One of the main activities under this award will be to develop theoretical and computational toolboxes for the discovery and characterization of such quantum mechanical states in models and materials which may stimulate experimental inquiry. This project includes mentoring and training students and junior researchers at the frontier of condensed matter physics using a variety of advanced analytical and numerical techniques.TECHNICAL SUMMARY:This award supports theoretical research and education in theoretical condensed matter physics to investigate phases of quantum matter. Discoveries of quantum Hall fluids and also of numerous strongly correlated materials unveiled the richness of possible quantum many-body phenomena. The recent discovery of topological insulators together with advances in strongly correlated systems have even emboldened the community to contemplate complete classification of all quantum many-body phases. While great progress has been made for non-interacting or weakly-interacting electrons, properly describing strong interactions is crucial for any such larger endeavors, but this is also where the available tools are quite limited. Duality approaches have contributed significantly to understanding systems of strongly interacting bosons, in particular of fractionalized phases. Tractable models, which are either exactly solvable or numerically accessible, have provided another avenue for explorations of possible topological phases. The PI will continue to combine these approaches to construct explicit models that realize so-called symmetry-protected topological phases and to discover their fractionalized counterparts. The PI will study new phases that emerge as well as phase transformations involving them.While the goal of classifying gapped phases may be in sight, there is a vast poorly understood terrain of gapless states in strongly correlated systems, which are also of great experimental interest. Examples include heavy fermion materials near criticality, strange metal and pseudogap behaviors in high-temperature cuprate superconductors, composite fermi liquid state of the quantum Hall fluid at half-filling, and gapless spin liquid states in 2D organic materials. Recent advances in understanding three dimensional symmetry-protected topological phases have shed unexpected new light on this landscape: A long-standing problem of particle-hole symmetry of the composite fermi liquid state was related to physics of strongly correlated phases on surfaces of 3D topological insulators. At the same time, developments in Density Matrix Renormalization Group has allowed numerical studies of the composite fermi liquid with unprecedented detail. The PI will attack problems in this context. The PI will examine broader application of the fermionic dualities and investigate gapless fractionalized phases with emphasis on experimentally motivated questions for candidate spin liquid materials and sharp questions in controlled models. This project includes mentoring and training students and junior researchers at the frontier of condensed matter physics using a variety of advanced analytical and numerical techniques.