NSF Award
2424315
NONTECHNICAL SUMMARY<br/><br/>This award supports research and education activities with a goal to develop a fundamental understanding of quantum phases of matter with many interacting particles, using the concepts of symmetry and topology. Symmetry is a fundamental aspect of a physical system and has been recognized as a powerful principle in modern theoretical physics. A familiar example is the fact that total electric charge is conserved in everyday physical processes, which can help distinguish between electric conductors, insulators and superconductors. In the realm of quantum mechanics, a system of interacting particles, such as electrons, can form unusual quantum states, in which the constituent particles move collectively in highly intricate patterns, making them resilient to small changes in external conditions. Deciphering these subtle patterns requires ideas from topology, a branch of mathematics that concerns properties of geometric shapes that are unchanged by smooth deformations. A deeper understanding of these quantum states may enable new schemes in harnessing quantum materials and designing quantum devices. <br/><br/>This project will leverage the power of the symmetry principle to advance the knowledge of exotic quantum states. The first thrust will investigate the properties of "symmetry defects", which are specific disturbances introduced to the system to reveal its underlying symmetry. Studying how the system reacts to such changes provides new methods to observe and characterize the unique quantum properties of the states involved. In the second thrust, the focus will be on the relationship between physical properties of a quantum crystal and microscopic interactions at the atomic level. This will furnish new perspectives on how crystalline quantum materials can be modeled theoretically. In the last thrust, the project will explore how the quantum behaviors of many interacting particles are affected by their interactions with the environment. Progress on this front will be crucial in exploiting these quantum states as memory for quantum information processing.<br/><br/>This award also supports the PI's educational and outreach activities through mentoring and training of graduate students and postdocs in theoretical condensed matter research; writing pedagogical review articles and organizing conferences and workshops; outreach to K-12 students and the general public.<br/><br/><br/>TECHNICAL SUMMARY<br/><br/>This award supports research and education activities with a goal to advance knowledge about quantum phases of matter with global symmetry and many-body topology as guiding principles. Characterizing the emergence of quantum phases from complex interactions between microscopic degrees of freedom represents a key challenge in quantum science. Advances in both condensed matter physics and quantum information science have significantly broaden the scope of quantum phases and provided new settings where universal behaviors of quantum many-body systems can arise.<br/> <br/>The project has three main thrusts: 1) Systematically develop a theory for a new type of non-local observables, called the disorder operators. These operators probe the fluctuations of symmetry charges in a given spatial region of the system, whose scaling behavior contains universal information about the underlying quantum state. The team will study how subleading corrections to the disorder operator depend on microscopic details, and develop field-theoretic techniques to compute them at quantum critical points. 2) Examine new aspects of UV/IR mixing: The interplay between microscopic conditions in lattice systems and macroscopic observables will be examined using the newly developed perspective of topological defects. The project will study how anomaly of a low-energy theory manifests in lattice quantum numbers and, conversely, how anomalous fractonic symmetries constrain low-energy dynamics. 3) Symmetry breaking and topological order in open quantum systems: the research team will investigate a new kind of symmetry breaking in mixed-state quantum phases and its implications on equilibration dynamics, and explore many-body topological order in quantum states under decoherence and beyond. <br/> <br/>This award also supports the PI's educational and outreach activities through mentoring and training of graduate students and postdocs in theoretical condensed matter research; writing pedagogical review articles and organizing conferences and workshops; outreach to K-12 students and the general public.<br/><br/>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.
