This CAREER award supports theoretical research and education in novel quantum phases of matter. Interacting many-electron systems, such as those found in a great variety of materials, are distinguished in that they exhibit emergent behaviors and properties that do not manifest in systems comprised of only few particles. The resulting rich variety of phases of matter with wildly different physical properties, e.g. conducting vs. insulating, many forms of magnetism, etc., underlie important technological applications of solid-state materials. An organizing principle that has proven extremely successful for describing conventional phases of matter is based on the notion of symmetry. However, exotic phases of matter have been discovered recently that transcend conventional wisdom and which are enabled by quantum-mechanical effects and strong interactions. Examples include the fractional quantum Hall effect that occurs when electrons are confined in a plane in an external magnetic field, and liquid-like states of magnetic moments in magnetic materials. These new phases of matter have remarkably rich and ordered, in a sense, internal structure, which is termed "topological order".
This project aims to advance the theoretical understanding of topologically ordered phases. The PI will investigate how the interplay between symmetry and topological order gives rise to new quantum phenomena, by developing a theoretical framework to systematically study topological phenomena in the presence of symmetries and to characterize new quantum phases of matter enriched by symmetries. With these insights the PI will also explore new ways to probe topological order in experiments.
The project will achieve broad impact beyond the condensed matter community, as the research touches on problems that are of fundamental interest in related fields, such as high-energy physics and mathematics. Beyond research, the project will seek to enrich physics education in local communities with coordinated outreach activities. Through integration with the Pathways to Science program at Yale, the outreach activities supported by this project will provide opportunities to middle- and high-school students from underrepresented groups in physics and STEM-related fields, as well as to the general public, aiming to elucidate the physics underlying this research, and more broadly to promote awareness of cutting-edge research on quantum materials.
This CAREER award supports research and education towards advancing fundamental understanding of quantum phases of matter in interacting many-body systems. In recent times, a synthesis between symmetry and topological order has brought new insights into the subject, unifying several important threads in the study of quantum matter. This research focuses on identifying the multifaceted roles of symmetries in exotic topological phases of matter and on characterizing universal quantum phenomena in these systems. The PI will use analytical methods supplemented by numerical simulations to tackle these problems. Specifically, this project has the following objectives:
1) Developing a theoretical framework for symmetry-enriched topological phases in fermionic systems. This includes a general classification of symmetry transformations on emergent excitations and potentially new quantum anomalies. Along the way, the PI will also investigate intrinsically interacting fermionic symmetry-protected topological phases in three dimensions, and will develop theoretical machinery to understand global phase diagrams around symmetric topological phases.
2) Developing a physical classification of gapped quantum field theories in three spatial dimensions, and characterizing quantum statistics of loop excitations. Another important aspect of this investigation is to advance new understanding of fracton topological phases by unraveling their deep connections to translation-symmetry-enriched topological order, with potential applications to spin liquid materials.
3) Investigating novel experimental probes of topological phases using dynamical measurements, building on the theoretical insights gained in this project. The PI plans to explore experimental signatures of symmetry fractionalization in dynamical and local measurements.
The project will achieve broad impact beyond the condensed matter community, as the research touches on problems that are of fundamental interest in related fields, such as high-energy physics and mathematics. Beyond research, the project will seek to enrich physics education in local communities with coordinated outreach activities. Through integration with the Pathways to Science program at Yale, the outreach activities supported by this project will provide opportunities to middle- and high-school students from underrepresented groups in physics and STEM-related fields, as well as to the general public, aiming to elucidate the physics underlying this research, and more broadly to promote awareness of cutting-edge research on quantum materials.
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.
