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Interplay of Topology and Geometry in Fractional Quantum Hall Liquids

Kun Yang from Florida State University, National High Magnetic Field Laboratory, presented this colloquium on April 6, 2022. Fractional Quantum Hall Liquids (FQHL) are the ultimate strongly correlated electron systems, and the birthplace of topological phase of matter. Early theoretical work has emphasized the universal or topological aspects of quantum Hall physics. More recently it has become increasingly clear that there is very interesting bulk dynamics in FQHL, associated with an internal geometrical degree of freedom, or metric. The appropriate quantum theory of this internal dynamics is thus expected to take the form of a "quantum gravity," whose elementary excitations are spin-2 gravitons. After briefly reviewing the topological aspect of FQHL, Yang will discuss in this talk how to probe the presence of this internal geometrical degree of freedom experimentally in the static limit, and detect the graviton excitation in spectroscopic measurements, in particular how to reveal its chirality. Comparison will be made with recent experimental and numerical work, and discussions on future experimental probes of the graviton chirality as well as its significance will be presented.