CAREER: Symmetry, Topology, and Transport in Strongly Interacting Quantum Many-Body Systems

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NONTECHNICAL SUMMARYThis CAREER award supports research and education on fundamental questions in quantum condensed matter systems and their applications to quantum computing. A central question in physics is to understand how matter can collectively organize itself into many different types of ordered phases. The transformation of water into ice is a common example. The study of liquids, crystals, magnets, superconductors, and other such phases of matter has revolutionized our understanding of matter itself and the technological basis of our society. The last decade has seen a renaissance in our ability to theoretically understand and experimentally probe novel quantum states of matter that do not exhibit conventional types of organization, but which are rather characterized by a subtler quantum topological order. The phenomena exhibited by these quantum states of matter can potentially be harnessed for a variety of quantum technologies, including quantum computers, which would be able to solve certain computational tasks exponentially more efficiently than classical computers. The theoretical tools to describe these phenomena are currently under rapid development and require basic advances. The PI and his group will pursue a multifaceted research program to tackle foundational theoretical questions, and to address the question of characterizing distinct possible quantum states of matter and their collective phenomena. These will then be pursued further in the context of specific materials and experimental settings. Finally, the theoretical insights gained will be applied to devise new ways of protecting delicate quantum states from their external environment, in order to advance the pursuit of scalable, fault-tolerant quantum computers. The research project has significant impact not only on the condensed-matter community, but also on high-energy physics, mathematics, quantum information, and potentially in industry in the area of quantum computing. The research will be carried out primarily with graduate students and postdoctoral scholars, whose training will benefit from the wide and advanced scope of the projects. The PI plans to also mentor undergraduate students to study these topics, and to maintain contact with the local K-12 community through a number of outreach activities organized by the Joint Quantum Institute and Physics Frontier Center at the University of Maryland, with the aim of increasing the participation of women and underrepresented minorities in STEM fields. TECHNICAL SUMMARYThis CAREER award supports research and education on fundamental questions in strongly interacting quantum many-body systems and their applications to quantum computing. Recent years have seen a renaissance in our ability to theoretically characterize and experimentally probe novel quantum states of matter and their excitations. This progress includes an understanding of new types of topological defects that can occur in strongly interacting fractionalized phases of matter. The universal properties of these defects are characterized within a recently been developed theoretical framework that incorporates the interplay of symmetry and topology in strongly interacting quantum liquids. The research focuses on the following main objectives:(1) Further developing the understanding of the physics of these new types of topological line- and point-defects and how they can be studied by using realistic model Hamiltonians, and be realized and probed experimentally in graphene fractional quantum Hall systems, and quantum spin-liquid materials. (2) Developing a comprehensive theoretical framework to characterize and describe symmetric topological phases of matter. The current theory must be extended to incorporate situations of physical interest, such as where the symmetries include space-time symmetries and can be anti-unitary and/or continuous, and also situations where the microscopic constituents are fermions. The ultimate goal is to develop a complete list of topological invariants that fully characterize strongly interacting topological quantum states of bosons and fermions with symmetry. An important aspect of this investigation will be to subsequently apply the insights gained to our understanding of quantum critical phenomena as well. (3) Developing applications of defects and symmetry-enriched topological states to quantum computation. Specifically, all scalable approaches to quantum error correction with local interactions rely heavily on topological states of matter for fault-tolerance and thus can benefit from the advances in our understanding of defects and symmetry in topological states. (4) Studying hydrodynamic thermal and electrical transport behavior in metallic and quantum critical systems. The research project has significant impact not only on the condensed-matter community, but also on high-energy physics, mathematics, quantum information, and potentially in industry in the area of quantum computing. The research will be carried out primarily with graduate students and postdoctoral scholars, whose training will benefit from the wide and advanced scope of the projects. The PI plans to also mentor undergraduate students to study these topics, and to maintain contact with the local K-12 community through a number of outreach activities organized by the Joint Quantum Institute and Physics Frontier Center at the University of Maryland, with the aim of increasing the participation of women and underrepresented minorities in STEM fields.