Quantum impurity model for anyons
Abstract
One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have not yet been unambiguously detected in experiment. Here we introduce a simple quantum impurity model, where bosonic or fermionic impurities turn into anyons as a consequence of their interaction with the surrounding manyparticle bath. A cloud of phonons dresses each impurity in such a way that it effectively attaches fluxes or vortices to it and thereby converts it into an Abelian anyon. The corresponding quantum impurity model, first, provides a different approach to the numerical solution of the manyanyon problem, along with a concrete perspective of anyons as emergent quasiparticles built from composite bosons or fermions. More importantly, the model paves the way toward realizing anyons using impurities in crystal lattices as well as ultracold gases. In particular, we consider two heavy electrons interacting with a twodimensional lattice crystal in a magnetic field, and show that when the impuritybath system is rotated at the cyclotron frequency, impurities behave as anyons as a consequence of the angular momentum exchange between the impurities and the bath. A possible experimental realization is proposed by identifying the statistics parameter in terms of the meansquare distance of the impurities and the magnetization of the impuritybath system, both of which are accessible to experiment. Another proposed application is impurities immersed in a twodimensional weakly interacting Bose gas.
 Publication:

Physical Review B
 Pub Date:
 October 2020
 DOI:
 10.1103/PhysRevB.102.144109
 arXiv:
 arXiv:1912.07890
 Bibcode:
 2020PhRvB.102n4109Y
 Keywords:

 Condensed Matter  Quantum Gases;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 19 pages, 5 figures