Strong Interactions, Topology, and Constraints in Emerging Phases of Matter

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NONTECHNICAL SUMMARYThis award supports research and education towards understanding the properties of new phases of matter in three dimensions, and the dynamics of low-dimensional quantum systems. One of the frontiers of modern physics is understanding what new types of quantum phenomena can occur in systems with many interacting particles. Striking examples of such phenomena discovered in the 20th century include superfluidity, superconductivity, and the fractional quantum Hall effect, all of which entail macroscopic numbers of interacting particles entering a coherent quantum state. More recently, rapid progress in our understanding of how specific abstract properties (in technical terms, topological properties) of quantum many-particle systems influence their real physical properties has led to the discovery of new classes of materials, such as topological insulators and superconductors. The latter, in particular, have drawn interest as a potential platform for quantum computing, in which information can be stored in a way that is intrinsically robust to random noise.The research focuses on two themes that are of current interest both for expanding our understanding of new types of possible quantum phenomena, and for investigating how strong interactions can potentially help identify promising platforms for quantum computing. The first theme is expanding our understanding of how topological properties can lead to new types of interacting quantum matter in three dimensions. The second theme is understanding how strong interactions, and ultimately the kinds of topological properties that are already well-understood in these systems, help shape how quantum systems evolve in time at finite temperature.The project will contribute to the workforce of highly trained STEM professionals both by training graduate students, and through programs and events coordinated by the PI focused on facilitating the transition of interested physics undergraduate and graduate students at the University of Minnesota to jobs in the private sector. This includes working with engineering departments to allow interested physics undergraduates to participate in senior engineering design projects, as well as helping coordinate extracurricular networking and career-information events aimed specifically at physics students.TECHNICAL SUMMARYThis award supports research and education towards understanding the role of topology and constraints in two areas: new phases of matter in three dimensions, and the dynamics of low-dimensional systems. In the area of phases of matter in three dimensions, the proposed research will focus on recently discovered fracton phases of matter, with the unusual feature that their low-lying excitations have restricted mobility. A combination of field-theoretic techniques and tools for analyzing group cohomology developed in the study of interacting symmetry-protected phases of matter will be used to address the following questions. First, what field theories exhibit the qualitative features of fracton phases? Second, when does symmetry in these and related systems lead to protected gapless boundary modes? Addressing these questions will expand our understanding of how the interplay between geometry and topology in these systems leads to physical properties qualitatively unlike those of other three-dimensional quantum phases.In the area of dynamics in low-dimensional systems, the focus will be on exploring the impact of constraints and topological order on dynamics. The proposed research will use a combination of numerical (exact diagonalization) and analytical approaches based in perturbation theory and random-matrix theory. As low-dimensional systems that approximate constrained systems become experimentally accessible, clarifying whether, when, and how constraints can lead to unusually slow dynamics in quantum many-body systems can significantly advance our understanding of how information can be more robustly stored at intermediate time-scales in quantum many-body systems. The project will contribute to the workforce of highly trained STEM professionals both by training graduate students, and through programs and events coordinated by the PI focused on facilitating the transition of interested physics undergraduate and graduate students at the University of Minnesota to jobs in the private sector. This includes working with engineering departments to allow interested physics undergraduates to participate in senior engineering design projects, as well as helping coordinate extracurricular networking and career-information events aimed specifically at physics students.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.