CAREER: Topological quantum devices as a window into strongly correlated matter

About This Grant

NONTECHNICAL SUMMARY A central challenge for quantum materials is understanding how large numbers of electrons interact and organize themselves into collective quantum states. These interactions often lead to emergent behavior, where the system exhibits new properties that are more than those of the sum of its parts. Well-known examples include superconductivity, which enables electric current to flow without resistance, and magnetism, which enables materials to generate magnetic fields. These phenomena have led to mature applications in technologies such as medical imaging and magnetic storage. Even more exotic is the phenomenon of charge fractionalization, where the material behaves as if its electrons have split up and carry a fraction of the electron charge. Such effects could potentially be harnessed to enable noise-resilient quantum information processing. Recent advances in experimental techniques have made it possible to fabricate and measure mesoscopic-scale quantum devices that serve as simplified yet powerful platforms for studying these interactions. This project seeks to deepen our understanding of theoretical models and to bridge the gap between theory and experiment by making testable predictions using advanced analytical and numerical techniques. By predicting signatures of complex electron interactions in relatively simple quantum devices, the research will propose new approaches to create and probe electronic states that go beyond conventional theories. The project also emphasizes education and workforce development. Graduate and undergraduate students will receive training in advanced theoretical and computational methods and will participate in research at the frontiers of quantum science. Outreach and classroom activities will include hands-on demonstrations of quantum entanglement and the development of a modern course on superconductivity, both available to the general public. These efforts aim to broaden public understanding of quantum physics and prepare a highly skilled quantum workforce, strengthening U.S. leadership in quantum information science. TECHNICAL SUMMARY This project investigates strongly correlated quantum systems through the theoretical study of quantum impurity models where both the impurity and its environment can be topologically nontrivial. These systems are perhaps the simplest examples that exhibit rich physics including non-Fermi liquid behavior, emergent anyonic excitations, and unconventional symmetry structures beyond SU(2). Recent advances in mesoscopic device fabrication and materials development have made it possible to probe these paradigmatic models experimentally, while theoretical progress has revealed new opportunities to explore the interplay of topology, symmetry, and electron correlations. The project aims to bridge the gap between theory and experiment by making testable predictions using analytical and numerical techniques. The research will focus on elucidating electron correlations and topology through quantum transport in mesoscopic devices, probing topological boundary excitations using quantum impurities, and developing new tools to study correlated multi-impurity states. The work combines quantum many-body and linear response theory, conformal field theory techniques, as well as numerical methods such as density matrix renormalization group. A key goal is to clarify the properties of emergent anyons in quantum impurity models, including Kondo anyons that arise in gapless systems and exhibit nontrivial impurity entropy, and to determine how their behavior compared to anyons in gapped topologically ordered phases. The project also emphasizes education and workforce development. Graduate and undergraduate students will receive training in advanced theoretical and computational methods and will participate in research at the frontiers of quantum science. Outreach and classroom activities will include hands-on demonstrations of quantum entanglement and the development of a modern course on superconductivity, both available to the general public. These efforts aim to broaden public understanding of quantum physics and prepare a highly skilled quantum workforce, strengthening U.S. leadership in quantum information science. 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.