Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions

Abstract

We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of ${\xi }_{\text{Moore-Read}}=1.30(5)$ and ${\xi }_{\text{anti-Pfaffian}}=1.38(14)$, in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to $56$ particles.

arXiv comment13 pages, 9 figures, published version

References in corpus (57)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• 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
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• On the low energy properies of fermions with singular interactions
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• The half-filled Landau level: the case for Dirac composite fermions
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• 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
• Landau level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Paired composite fermion wavefunctions
• Parton construction of a wave function in the anti-Pfaffian phase
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• 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
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Spinful Composite Fermions in a Negative Effective Field
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Composite Dirac liquids: parent states for symmetric surface topological order
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Mirror symmetry and the half-filled Landau level
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• A controlled expansion for certain non-Fermi liquid metals
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Fermi-sea-like correlations in a partially filled Landau level
• 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
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Lattice Monte Carlo for Quantum Hall States on a Torus
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Emergent particle-hole symmetry in the half-filled Landau level
• Trial wave functions for a Composite Fermi liquid on a torus
• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
• Particle-Hole Symmetry and the Fractional Quantum Hall States at 5/2 Filling Factor
• Dirac Composite Fermion - A Particle-Hole Spinor

Cited by in corpus (20)

• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Composite fermion pairing induced by Landau level mixing
• Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying non-Abelian anyons with upstream noise
• 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
• 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
• 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
• Topological pairing of composite fermions via criticality
• Non-Abelian phases from the condensation of Abelian anyons
• The Second Landau Level Projection of Antiholomorphic Pfaffian Wavefunctions