Novel Topological States in Correlated Quantum Systems

Boston College, Chestnut Hill MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education in understanding novel quantum states of matter in solid-state materials. At low temperatures, quantum mechanics can bring materials into states of matter that have no classical analog. Topological states of matter are such novel quantum states of matter, and they exhibit striking new physical properties. For example, charge carriers in some topological states behave as if they were a fraction of an electron, and their properties can be exploited to build robust quantum computers. The thrusts of the research activities include: 1) Developing a new theoretical framework to systematically understand topological states and developing new computational techniques to simulate these states in a reliable fashion. 2) Applying these techniques to investigate topological states and their physical properties in real materials. 3) Developing guiding principles helpful in searching for new topological states in materials. This project will generate knowledge and computational methods needed for advances in quantum material science and quantum technology. The educational activities include developing pedagogical courses, lectures, and journal-club series for undergraduate and graduate students, with emphasis on the new states of matter discovered in modern condensed matter physics. As an outreach activity, an interactive website will be created to disseminate teaching materials and to demonstrate topological phenomena, with the aim of sparking general interest in science and technology. TECHNICAL SUMMARY This award supports theoretical research and education in understanding topological quantum states of matter. Very rich classes of correlation-driven topological phases have been predicted theoretically; however, the existence of only few of them has been confirmed in real materials. The relevant challenges are the limitations of currently available theoretical and numerical methods for correlated quantum systems, as well as the lack of physical guiding principles to direct the search for many correlated topological states. This project addresses both these challenges. The research activities comprise three main thrusts: 1) The PI will further develop a symmetric tensor network framework and numerical algorithms suitable for investigating correlated topological phases. The tensor network can be viewed as a new language for quantum many-body physics capable of capturing topological properties of quantum states. 2) By applying this framework, the PI will search for model systems that realize correlation-driven topological phases, including models for correlated transition-metal materials. In addition, excitation properties of candidate topological materials will be computed and compared with experiments. 3) The PI will develop symmetry-based guiding principles that are independent of microscopic details, aiding the search for topological states in materials. The research is closely connected to quantum information science and algebraic topology in mathematics, and it could bring new insight in these disciplines. The educational activities include developing pedagogical courses, lectures, and journal-club series for undergraduate and graduate students, with emphasis on the new states of matter discovered in modern condensed matter physics. The PI will develop and maintain an interactive website hosting research and teaching materials, which will include demonstrations of topological phenomena in condensed matter physics and tensor networks. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.