Symmetry-induced 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 work 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 Laughlin-type 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.

published version, added a section discussing a mathematical framework which generalizes to arbitrary Abelian topological order

References in corpus (3)

• Non-Abelian Anyons and Topological Quantum Computation
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State

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• Folding approach to topological orders enriched by mirror symmetry
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases