CAREER: Quantum Information Theory of Many-body Physics

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In nature, systems of strongly interacting quantum mechanical particles can form a novel phase of matter in which the constituents of the system are strongly entangled with each other. While such phases can have potentially transformative applications, such as building a topologically protected fault-tolerant quantum computer, the presence of such entanglement has posed a significant challenge in our understanding, characterization, and experimental identification of such phases. The PI will address these issues by leveraging a novel theoretical framework known as the entanglement bootstrap program, which was pioneered by the PI. This theoretical framework will lead to the development of efficient methods to identify and characterize strongly entangled phases of matter in experiments and in many-body simulations on classical computers. The PI will also develop a comprehensive education and outreach plan, which includes an education and training of a graduate student and a postdoctoral scholar. Moreover, the research activities will be disseminated in a form that is accessible to a broad set of researchers. Finally, the PI will host a bootcamp on quantum computing and quantum entanglement geared towards college students of underrepresented backgrounds near Davis, California, broadening the participation of students of diverse backgrounds to the field of quantum information science. The main scientific goal of this proposal is to develop a theoretical framework that can predict properties of strongly entangled quantum many-body systems at long wavelength from their local data, encoded in local reduced density matrices. Leveraging the recent development in the entanglement bootstrap program, the PI will make progress on the following problems. First, the PI will discover the topological invariants that can characterize many-body quantum phases. Second, the PI will develop a method to extract these topological invariants from the data that are readily available from numerical studies and experiments. Finally, by studying solutions to the quantum marginal problem, the PI will develop numerical methods to simulate and interpret low-energy properties of interacting quantum many-body systems. This project is jointly supported by the NSF Division of Physics and the NSF Division of Materials Research.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.