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

References in corpus (10)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State
• The electron lifetime in Luttinger liquids
• Edge excitations and Topological orders in rotating Bose gases
• Trapping Abelian anyons in fractional quantum Hall droplets

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• Experimental probe of topological orders and edge excitations in the second Landau level
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Observable Bulk Signatures of Non-Abelian Quantum Hall States
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• Competing ν= 5/2 fractional quantum Hall states in confined geometry
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states
• Thermopower of Quantum Hall States in Corbino Geometry as a Measure of Quasiparticle Entropy
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• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Improved phase gate reliability in systems with neutral Ising anyons
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization
• Phase diagram and edge states of the $\nu =5/2$ fractional quantum Hall state with Landau level mixing and finite well thickness
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Tracing non-Abelian anyons via impurity particles
• Quantum Hall ferromagnetic states and spin-orbit interactions in the fractional regime
• Fractional angular momentum and anyon statistics of impurities in Laughlin liquids
• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
• Topological blockade and measurement of topological charge
• Probing quantum phases in ultra-high-mobility two-dimensional electron systems using surface acoustic waves
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Distinguishing particle-hole conjugated Fractional Quantum Hall states using quantum dot mediated edge transport
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Anyonic braiding via quench dynamics in fractional quantum Hall liquids
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude
• Dynamics of Quantum Hall Interfaces
• Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Landscapes of an out-of-equilibrium anyonic sea
• Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids
• Thermoelectric Hall conductivity of the fractional quantum Hall systems on a disk
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Refermionized theory of the edge modes of a fractional quantum Hall cloud