Topological and critical states of matter in strongly correlated electronic systems

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Topological and critical states of matter are of fundamental importance and are likely to have a huge impact on the future quantum technology. These novel states of matter are purely quantum and are sharply distinct from conventional states of matter that fall in the classical symmetry breaking paradigm. In recent years, we have witnessed great developments in the theory of these novel states. However, there are still two major challenges in the community: (1) to realize interacting topological phases in real materials; (2) to understand the precise properties of critical states of matter. These problems are intrinsically strongly interacting and non-perturbative, which poses difficult obstacles for the community to solve them using conventional methods. The goals of my research are to tackle these two challenges by employing both non-perturbative numerics and quantum field theory analysis. ******Topological and critical states of matter have many novel properties. Quantum spin liquids, for example, exhibit an exotic phenomenon called spin-charge separation, in which the electrons are fractionalized into two particles, namely the spinon and chargon. The spinon is carrying spin-1/2 without any electric charge, while the chargon carries one electric charge without any spin. This novel property may have important applications, such as topological quantum computation and understanding high-temperature superconductors. My proposed research will study the theory of spin liquids and other strongly correlated system using numerical methods (DMRG, Monte Carlo) and analytical quantum field theory analysis.******My research program will build a bridge between abstract theory and real experiments, and it will also connect different areas of physics. This research will enable condensed matter systems to be a table-top experimental platform to study interesting quantum field theories, and it will help to resolve open questions in both condensed matter and high energy physics. Besides the impact on fundamental science, my research will also likely to have an impact on technology, since novel quantum phases of matter will be critical for future quantum technology. Understanding strongly correlated materials can pave the way towards understanding high-temperature superconductors and serve as a guide in the search for a room temperature superconductor. This could have a large technological and practical impact on the devices, transportation, and energy industries of the future.******The research will also contribute to training students and researchers with both advanced numerical and theoretical skills. The combination of these two skills will give them unique advantages, enabling them to make important contributions to theoretical condensed matter physics. These skills will also prepare them for material science and industry. For example, the skills of numerical simulations and data analysis will be useful for occupations in finance and software engineering. **