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

TL;DR

This paper develops an exact bosonization scheme for anyons in fractional quantum Hall systems, enabling dual bosonic descriptions of various phases and revealing new topological states with potential experimental relevance.

Contribution

It introduces a novel exact bosonization method for anyons in quantum Hall fluids, allowing explicit derivation of statistical interactions and discovery of new topological phases.

Findings

Derived explicit microscopic statistical interactions for anyons.

Identified new topological phases in bosonic fractional quantum Hall states.

Numerical analysis supports the existence of these phases.

Abstract

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.