Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model

Abstract

We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $\nu =5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We also mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. From the evolution of edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle (with charge $\pm e/4$) when propagating at the edge; using numbers obtained from a specific set of parameters we estimate the decoherence length to be around four microns. This sets an upper bound for the separation of the two point contacts in a double point contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge) while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).

15 pages, 9 figures; Estimate of e/4 quasiparticle/hole coherence length when propagating along the edge modified in response to a recent revision of Ref. 25, and minor changes elsewhere

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Cited by in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• The non-Abelian Interferometer
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Thermopower as a Possible Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall Liquids
• Observable Bulk Signatures of Non-Abelian Quantum Hall States
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Quantum Hall ferromagnetic states and spin-orbit interactions in the fractional regime
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States