Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect

Abstract

The particle-hole (PH) symmetry of {\em electrons} is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. This article investigates an emergent symmetry in the fractional quantum Hall effect, namely the PH symmetry of {\em composite fermions}, which relates states at composite fermion filling factors ${\nu }^{\ast }=n+\bar{\nu }$ and ${\nu }^{\ast }=n+1-\bar{\nu }$, where the integer $n$ is the $\Lambda$ level index and $0\le \bar{\nu }\le 1$. Detailed calculations using the microscopic theory of composite fermions demonstrate that for low lying $\Lambda$ levels (small $n$): (i) the 2-body interaction between composite-fermion particles is very similar, apart from a constant additive term and an overall scale factor, to that between composite-fermion holes in the same $\Lambda$ level; and (ii) the 3-body interaction for composite fermions is an order of magnitude smaller than the 2-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low $\Lambda$ levels, which is also supported by exact diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors $\nu =\frac{n+\bar{\nu }}{2(n+\bar{\nu })\pm 1}$ and $\nu =\frac{n+1-\bar{\nu }}{2(n+1-\bar{\nu })\pm 1}$, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing $\Lambda$ level index, the 2-body and 3-body pseudopotentials become comparable, but at the same time they both diminish in magnitude, indicating that the interaction between composite fermions becomes weak as we approach $\nu =1/2$.

9 pages, 3 figures, 2 tables

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Cited by in corpus (12)

• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Composite fermion pairing induced by Landau level mixing
• Half-integer conductance plateau at the $\nu =2/3$ fractional quantum Hall state in a quantum point contact
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Dihedral twist liquid models from emergent Majorana fermions
• Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations