Virtual Workshop Quantum Hall Effect: Status Report: May 3-7, 2021

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Organized by: A. Gromov, G. Csáthy, F.D.M. Haldane, S. Simon, D. Son.

Two-dimensional electron system (2DES) in a strong magnetic field exhibits extraordinary rich variety of phenomena that arise from the strong interactions between the electrons. Among these phenomena, the most notorious one is the fractional quantum Hall (FQH) effect, which is the major playground for investigation of the interplay between the strong interactions and topology. FQH systems support anyonic excitations – the quasiparticles that do not obey either Fermi or Bose statistics with the electric charge given by a
fraction of the charge of an electron. Perhaps the most remarkable properties of certain FQH states is that they support non-Abelian anyons. Obtaining control over these excitations is an essential step towards implementation of topological quantum computation paradigm.

FQH effect is notorious for defying analytical treatment due to its strongly interacting nature, which renders more traditional approaches based on perturbation theory ineffective. In turn, this leads to new ideas based on the topological quantum field theory (TQFT) and WZW/CS correspondence as well as conformal field theory. Groundstates of FQH systems provide real-world realization of TQFTs. 2DES also support strongly interacting gapless phases, known as unquantized Hall effect. These phases possibly provide the realization of the non-supersymmetric, fermionic dualities that have recently attracted a lot of attention from high energy and condensed matter community. Physics of 2DES has proven to be an extremely fertile ground for collaboration between the most abstract, ingenious theories and table top experiments. With the development of new materials and further improvement of the old ones it certainly holds many new surprises.

Although the field is very mature, it has experienced a boom of exciting experimental and theoretical advances over the last several years. The goal of the workshop is to discuss the new experimental developments and identify open questions and promising new directions in research on 2DES and FQH effect in particular. The proposed workshop will bring together the experimentalists who lead these breakthroughs and the theorists working in the field.