The breakdown of most conventional theoretical techniques is a hallmark of strongly correlated many-body systems. In particular, phases with fractional excitations and unconventional quantum phase transitions are not accessible by perturbative methods. There is thus a compelling need for alternative techniques. Among the most powerful tools available to study such systems are so-called dualities, which state that two apparently distinct theories are, in fact, one and the same. Crucially, many dualities relate systems that are hard to study to those that are much simpler and thus allow understanding the former by analyzing the latter.
Fractional quantum Hall states exhibit many fascinating aspects of quantum many-body physics in an experimentally available platform. The interplay between theory and experiment continues to yield surprising discoveries and has already kept this field vibrant over many decades. Among the biggest mysteries in quantum Hall physics is the plateau at ν=5/2, widely expected to host highly prized non-Abelian anyons. Unlike many other fillings, where theory and experiment agree even quantitatively, its identity remains hotly debated. Our group's current research on the fractional quantum Hall effect focuses on the ν=5/2 state via questions that range from interpreting or proposing concrete experiments to more abstract theoretical questions.
Conventional forms of magnetism are essentially classical phenomena: their ground states break symmetries, and quantum fluctuations only quantitatively affect the properties of the phases. Enhanced quantum effects can give rise to new phases of phenomena known as quantum spin liquids, which do not break symmetries but exhibit topological order. Such enhancements may occur when multiple classical states compete, e.g., at a phase transition or due to frustration. Our group works on determining the conditions that promote the formation of these phases and characterizing their properties.