Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian

Abstract

We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (`PH-Pfaffian') topological order, a phase consistent with the recently reported thermal Hall conductance [Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic $\nu =5/2$ quantum-Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the $\nu =5/2$ ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak $p$-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

6 pages, 4 figures

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Cited by in corpus (39)

• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
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• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
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• Quantum Hall hierarchy from coupled wires
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• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Composite fermion pairing induced by Landau level mixing
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• Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities
• Why is the HLR theory particle-hole symmetric?
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• PH-Pfaffian order in a translationally and rotationally invariant system
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Pfaffian paired states for half-integer fractional quantum Hall effect
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• 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
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Two-component parton fractional quantum Hall state in graphene
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• PH Pfaffian intra and inter correlations in the quantum Hall bilayer
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Non-Abelian phases from the condensation of Abelian anyons
• Topological pairing of composite fermions via criticality
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• The Second Landau Level Projection of Antiholomorphic Pfaffian Wavefunctions
• Dipole representation of composite fermions in graphene quantum Hall systems