Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field

Abstract

Motivated by the experimental observation of a quantized 5/2 thermal conductance at filling $\nu =5/2$, a result incompatible with both the Pfaffian and the Antipfaffian states, we have pushed the expansion of the effective Hamiltonian of the $5/2$ quantized Hall state to third-order in the parameter $\kappa =E_c/\hslash {\omega }_c\propto 1/\sqrt{B}$ controlling the Landau level mixing , where $E_c$ is the Coulomb energy and ${\omega }_c$ the cyclotron frequency. Exact diagonalizations of this effective Hamiltonian show that the difference in overlap with the Pfaffian and the AntiPfaffian induced at second-order is reduced by third-order corrections and disappears around $\kappa =0.4$, suggesting that these states are much closer in energy at smaller magnetic field than previously anticipated. Furthermore, we show that in this range of $\kappa$ the finite-size spectrum is typical of a quantum phase transition, with a strong reduction of the energy gap and with level crossings between excited states. These results point to the possibility of a quantum phase transition at smaller magnetic field into a phase with an emergent particle-hole symmetry that would explain the measured $5/2$ thermal conductance of the $5/2$ quantized Hall state.

arXiv comment10 pages + 5 p of appendix, all comments welcome

References in corpus (51)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of half-integer thermal Hall conductance
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Is the Composite Fermion a Dirac Particle?
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Thirty Years of Composite Fermions and Beyond
• Landau level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Parton construction of a wave function in the anti-Pfaffian phase
• Cooper Instability of Composite Fermions
• Isolated Ballistic Non-Abelian Interface Channel
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Novel method distinguishing between competing topological orders
• Landau Level Mixing in the Perturbative Limit
• Fractional quantum Hall effect and nonabelian statistics
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Quench dynamics and parity blocking in Majorana wires
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Striped quantum Hall state in a half-filled Landau level
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Electron Correlations in Partially Filled Lowest and Excited Landau Levels
• Geometric construction of Quantum Hall clustering Hamiltonians
• Energetics of Pfaffian-AntiPfaffian Domains
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Temperature enhancement of thermal Hall conductance quantization
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Thermal equilibration on the edges of topological liquids
• Local two-body parent Hamiltonians for the entire Jain sequence
• The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators
• Level crossings induced by a longitudinal coupling in the transverse field Ising chain
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description

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