The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics

Abstract

We review a recent development in the theoretical understanding of the nu=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with abelian statistics theta=pi/2, which obey complete spin-charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitudes of the chiral persistent currents in both states and show that they have different temperature dependence. Finally, we find indications of a classical two-step phase transition between the new and the Moore-Read states, through a compressible state, which is characterized by the spontaneous breaking of a hidden Z_2 symmetry corresponding to the conservation of the chiral fermion parity. We believe that this transition could explain the "kink" observed in the activation experiment for nu=5/2.

36 pages, 6 figures, Latex2e

References in corpus (4)

• Experimental Evidence for a Spin-Polarized Ground State in the ν=5/2 Fractional Quantum Hall Effect
• Paired fractional quantum Hall states and the nu=5/2 puzzle
• Experimental Demonstration of Fermi Surface Effects at Filling Factor 5/2
• Stability and Activation Gaps of Parafermionic Hall States in the Second Landau Level

Cited by in corpus (14)

• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
• Lepton Flavor Violation, Neutralino Dark Matter and the Reach of the LHC
• Non-abelian statistics from an abelian model
• A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states
• Paired states on a torus
• Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers
• Ultimate braid-group generators for coordinate exchanges of Ising anyons from the multi-anyon Pfaffian wave functions
• Aharonov-Bohm effect in the non-Abelian quantum Hall fluid
• Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux
• Computational equivalence of the two inequivalent spinor representations of the braid group in the Ising topological quantum computer
• Topological Quantum Computation with the universal R matrix for Ising anyons