An exactly solvable model for anyons with non-Abelian flux

Abstract

We present an exactly solvable model for synthetic anyons carrying non-Abelian flux. The model corresponds to a two-dimensional electron gas in a magnetic field with a specific spin interaction term, which allows only fully aligned spin states in the ground state; the ground state subspace is thus two-fold degenerate. This system is perturbed with identical solenoids carrying a non-Abelian gauge potential. We explore dynamics of the ground state as these solenoids are adiabatically braided and show they behave as anyons with a non-Abelian flux. Such a system represents a middle ground between the ordinary Abelian anyons and the fully non-Abelian anyons.

6 pages, 2 figures

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• An Open-System Quantum Simulator with Trapped Ions
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Fractional statistics in anyon collisions
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Anyonic interferometry and protected memories in atomic spin lattices
• Fractional charge and fractional statistics in the quantum Hall effects
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Induced self-stabilization in fractional quantum Hall states of light
• Emulating anyonic fractional statistical behavior in a superconducting quantum circuit
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Fractional angular momentum in cold atom systems
• Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
• Fractional statistics of topological defects in graphene and related structures
• Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity
• Tracing non-Abelian anyons via impurity particles
• Creation and manipulation of anyons in a layered superconductor-2DEG system