Anyonic statistics of quantum impurities in two dimensions

TL;DR

This paper shows that impurities in a two-dimensional quantum bath can behave as anyons with fractional statistics, breaking time-reversal symmetry and enabling potential realization of anyons in various physical systems.

Contribution

It introduces a novel framework where impurities in 2D baths act as flux-tube-charged-particle composites exhibiting fractional statistics.

Findings

Impurities induce an effective magnetic flux, breaking time-reversal symmetry.

A critical coupling causes a transition to anyonic behavior.

Potential realization of anyons in superfluid helium, phonons, and ultracold gases.

Abstract

We demonstrate that identical impurities immersed in a two-dimensional many-particle bath can be viewed as flux-tube-charged-particle composites described by fractional statistics. In particular, we find that the bath manifests itself as an external magnetic flux tube with respect to the impurities, and hence the time-reversal symmetry is broken for the effective Hamiltonian describing the impurities. The emerging flux tube acts as a statistical gauge field after a certain critical coupling. This critical coupling corresponds to the intersection point between the quasiparticle state and the phonon wing, where the angular momentum is transferred from the impurity to the bath. This amounts to a novel configuration with emerging anyons. The proposed setup paves the way to realizing anyons using electrons interacting with superfluid helium or lattice phonons, as well as using atomic impurities in ultracold gases.