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.

Figure 1

A schematic illustration of the bosonization of anyons in 2D.

Figure 2

(a) The black dots give the energy spectrum with 18 bosons, 11 orbitals, and a truncated Hamiltonian dual to ${\widehat{V}}_1^{2\mathrm{bdy}}$ as detailed in [36], and the fermionic spectrum of ${\widehat{V}}_1^{2\mathrm{bdy}}$ is shown here with red crosses as comparison. (b) The ground state entanglement spectrum, with low-lying states (shown in red) having the correct Virasoro counting.