Energy minimization of paired composite fermion wave functions in the spherical geometry

Abstract

We perform the energy minimization of the paired composite fermion (CF) wave functions, proposed by Möller and Simon (MS) [PRB 77, 075319 (2008)] and extended by Yutushui and Mross (YM) [PRB 102, 195153 (2020)], where the energy is minimized by varying the CF pairing function, in the case of an approximate model of the Coulomb interaction in the second Landau level for pairing channels $\ell =-1,3,1$ which are expected to be in the Pfaffian, anti-Pfaffian and particle-hole symmetric (PH) Pfaffian phases respectively. It is found that the energy of the $\ell =-1$ MS wave function can be reduced substantially below that of the Moore-Read wave function at small system sizes, however, in the $\ell =3$ case the energy cannot be reduced much below that of the YM trial wavefunction. Nonetheless, both our optimized and unoptimized wavefunctions with $\ell =-1,3$ extrapolate to roughly the same energy per particle in the thermodynamic limit. For the $\ell =1$ case, the optimization makes no qualitative difference and these PH-Pfaffian wave functions are still energetically unfavourable. The effective CF pairing is analyzed in the resulting wave functions, where the effective pairing for the $\ell =-1,3$ channels is found to be well approximated by a weak-pairing BCS ansatz and the $\ell =1$ wave functions show no sign of emergent CF pairing.

arXiv comment14 pages, 4 figures, 7 tables

References in corpus (42)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• 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
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• 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
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• 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
• Novel method distinguishing between competing topological orders
• Landau Level Mixing in the Perturbative Limit
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• 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
• Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• 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

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