The last decade has witnessed a revolution in the prediction and understanding of new phases of matter characterized by topology and entanglement. This includes topological insulators, semimetals, superconductors, quantum spin liquids, topological Kondo systems, etc.. However, most of the theory is directed at the classification of ground state properties and elementary excitations, and most successful experiments are spectroscopic. The big frontier is transport. The latter is the key for nearly all applications in condensed matter. It is also the most sensitive probe, and gives access to the lowest frequencies and energies. Yet its understanding remains much more primitive than that of many techniques, at a time when the body of transport experiments is rapidly growing. Responding to the need to tackle this problem extensively, the proposed ERC will provide a broad and detailed understanding of heat and electrical transport in a wide variety of quantum systems in various regimes: quantum magnets at low/high temperatures, near critical points, and semimetals. It will provide key tools and guidelines to study and understand transport in experiments.
I propose to focus on two goals that I deem most direly needed for the understanding of transport: 1. Develop the theory of thermal conductivity in complex magnets, both in quantum spin liquids and more generally at high temperatures and quantum critical points, 2. Investigate transport in novel conducting and superconducting states with controllable topology induced by spontaneous symmetry breaking phenomena.
Achieving these goals will enable informed interpretation of a growing body of modern experiments on correlated states. The proposed work will add to fundamental theory, develop new tools and methodologies, and forge ties to specific experiments, laying the groundwork for future applications. It will train students and postdocs in cutting-edge theory and the art of applying it to quantum materials.
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