Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect

Abstract

We present a method for the exact construction of the fully particle-hole symmetric PH-Pfaffian ground state and its charged excitations on a sphere. We adopt the Moore-Read state, but with a nonholomorphic pairing component as in previous studies, and project it to the lowest Landau level. We study the energetics as well as other properties of these states and find that in a pure system interacting with the Coulomb forces the PH-Pfaffian cannot compete with either the Moore-Read state or its particle-hole conjugate, the anti-Pfaffian state, as an explanation for the 5/2-effect.

References in corpus (14)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Energetics of Pfaffian-AntiPfaffian Domains
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$

Cited by in corpus (17)

• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Parametrization and thermodynamic scaling of pair correlation functions for the Fractional Quantum Hall Effect
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Two-component parton fractional quantum Hall state in graphene
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• PH Pfaffian intra and inter correlations in the quantum Hall bilayer
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids