ICMT Seminar: "Implications of Duality on Fractional Quantum Hall Transitions, Composite Fermi Liquids, and Fractional Topological Insulators"
(sign-up)Gil Cho, KAIS
Institute for Condensed Matter Physics
Employeeing the recently-developed field-theoretic (2+1)d dualities, we study strongly-correlated condensed matter systems, namely a clean fractional quantum Hall transitions (from a Laughlin state to a trivial insulator subject under the strong spatially-periodic potentials), composite Fermi liquid and surface of fractional topological insulators. Despite of long-held histories, all the three systems stand for the frontiers of our understandings of two- and three-dimensional topological phases. This is in a sharp contrast to the incompressible gapped fractional quantum Hall states, which are inarguably best-understood systems amongst various strongly-correlated quantum matter. The gapless matter contents in those systems essentially bar us to develop any reliable perturbative expansion and extract useful information. In this talk, we will show that the duality sheds some light on these systems and helps us to learn new physics about these quantum matters. For the transition, there are at least three widely-used historic descriptions, projective parton method, composite fermion theory, and composite boson theory. Among the three approaches, we show that the parton method provides a `parent' theory, which can be driven to composite particle theories and composite Fermi liquids. Using the dualities in combination with the coupled-wire method and the parton argument, we argue that the composite Fermi liquid can be obtained via a confinement from a critical point, which is naturally described by the parton method. This critical point is closely related to the surface of the time-reversal symmetric fractional topological insulators, for which we obtain a symmetric topologically-ordered surface state similar to the T-pfaffian state. While deriving the results, the duality plays an essential role and provides a unifying view on these three strongly-correlated systems.
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