Symmetryinduced anyon breeding in fractional quantum Hall states
Abstract
An exotic feature of the fractional quantum Hall effect is the emergence of anyons, which are quasiparticle excitations with fractional statistics. In the presence of a symmetry, such as U (1) charge conservation, it is well known that anyons can carry fractional symmetry quantum numbers. In this paper we reveal a different class of symmetry realizations, i.e., anyons can "breed" in multiples under symmetry operation. We focus on the global Ising (Z_{2}) symmetry and show examples of these unconventional symmetry realizations in Laughlintype fractional quantum Hall states. One remarkable consequence of such an Ising symmetry is the emergence of anyons on the Ising symmetry domain walls. We also provide a mathematical framework which generalizes this phenomenon to any Abelian topological orders.
 Publication:

Physical Review B
 Pub Date:
 March 2014
 DOI:
 10.1103/PhysRevB.89.115321
 arXiv:
 arXiv:1311.6481
 Bibcode:
 2014PhRvB..89k5321L
 Keywords:

 73.43.f;
 05.30.Pr;
 11.30.j;
 Quantum Hall effects;
 Fractional statistics systems;
 Symmetry and conservation laws;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 published version, added a section discussing a mathematical framework which generalizes to arbitrary Abelian topological order