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 (6)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Fractional Quantum Hall States and Jack Polynomials
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect

Cited by in corpus (10)

• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Odd- and even-denominator fractional quantum Hall states in monolayer WSe${}_2$
• 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
• Composite Fermion Mass
• Fixed-phase diffusion Monte Carlo study of the activation gap and the skyrmion excitation of $\nu =1$ system in the presence of charged impurities
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions