Statistical interactions and boson-anyon duality in fractional quantum Hall fluids*

We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that may be experimentally accessible. Numerical analysis of the energy spectrum and ground state entanglement properties are carried out for simple examples. We also discuss an exact unitary transformation between electrons and composite fermions and a fractal structure of the possible FQH states, as well as the experimental implications of anyon statistics in the presence of disorder. (Bo Yang, Phys. Rev. Lett. 127, 126406 (2021))