Surprising robustness of particle-hole symmetry for composite fermion liquids

Abstract

We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at $1/3$ and $2/3$. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.

References in corpus (30)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Fractional Quantum Hall States and Jack Polynomials
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• The half-filled Landau level: the case for Dirac composite fermions
• The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• A nu=2/5 Paired Wavefunction
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• 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
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• Composite fermi liquids in the lowest Landau level
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Generalized Quantum Hall Projection Hamiltonians
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect
• Unpaired composite fermion, topological exciton, and zero mode
• Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study
• Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
• Transference of Fermi Contour Anisotropy to Composite Fermions
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• The maximum density droplet to lower density droplet transition in quantum dots
• Construction of the edge states in fractional quantum Hall systems by Jack polynomial
• Fractional quantum Hall effect arising from repulsive three body interaction

Cited by in corpus (16)

• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Odd- and even-denominator fractional quantum Hall states in monolayer WSe${}_2$
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level
• Composite fermion pairing induced by Landau level mixing
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Automatic design of Hamiltonians
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Composite Fermion Mass
• Anomalous coupling between magnetic and nematic orders in quantum Hall systems
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Fixed-phase diffusion Monte Carlo study of the activation gap and the skyrmion excitation of $\nu =1$ system in the presence of charged impurities
• Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions