Anyonic statistics of quantum impurities in two dimensions

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.

Figure 1

(a) The spectral function of the relative angular motion of two impurities immersed in a 2D bath, ${\mathcal{A}}_M$, with $\tilde{E}=E/B$, and (b) the magnetic flux $\mathrm{\Phi }/\left(2\pi \right)$, as a function of the coupling constant $\tilde{\alpha }\equiv {\alpha }_F/\left(r{B}^2\right)$. The vertical dashed line indicates the critical coupling, after which the magnetic flux becomes constant and behaves as a statistical gauge field. See the text.

Figure 2

(a) After the critical coupling, (cf. Fig. 1), two impurities immersed in a two-dimensional bath behave as a charged particle orbiting around a magnetic flux tube in relative coordinates. The latter is the manifestation of the bath with respect to the impurities. Consequently, the angular momentum of the two impurities in relative coordinates becomes fractional. (b) Inside the bath, the impurities turn into flux-tube-charged-particle composites, and obey anyonic statistics upon exchange. See the text.