TY - JOUR

T1 - Particle-hole symmetry for composite fermions

T2 - An emergent symmetry in the fractional quantum Hall effect

AU - Balram, Ajit C.

AU - Jain, J. K.

N1 - Funding Information:
A.C.B. was supported in part by the European Research Council (ERC) under the European Union Horizon 2020 Research and Innovation Programme, Grant Agreement No. 678862, the Villum Foundation, and the Center for Quantum Devices funded by the Danish National Research Foundation. J.K.J. was supported by the U.S. National Science Foundation Grant No. DMR-1401636. Some calculations were performed with Advanced CyberInfrastructure computational resources provided by The Institute for CyberScience at The Pennsylvania State University. Some of the numerical calculations were performed using the diagham package, for which we are grateful to its authors.
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/12/29

Y1 - 2017/12/29

N2 - The particle-hole (PH) symmetry of 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. We investigate an emergent symmetry in the fractional quantum Hall effect, namely, the PH symmetry of composite fermions, which relates states at composite fermion filling factors ν∗=n+ν and ν∗=n+1-ν, where the integer n is the Λ-level index and 0≤ν≤1. Detailed calculations using the microscopic theory of composite fermions demonstrate the following for low-lying Λ levels (small n): (i) The two-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 Λ level; and (ii) the three-body interaction for composite fermions is an order of magnitude smaller than the two-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low Λ levels, which is also supported by exact-diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors ν=n+ν2(n+ν)±1 and ν=n+1-ν2(n+1-ν)±1, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing Λ-level index, the two-body and three-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 ν=1/2.

AB - The particle-hole (PH) symmetry of 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. We investigate an emergent symmetry in the fractional quantum Hall effect, namely, the PH symmetry of composite fermions, which relates states at composite fermion filling factors ν∗=n+ν and ν∗=n+1-ν, where the integer n is the Λ-level index and 0≤ν≤1. Detailed calculations using the microscopic theory of composite fermions demonstrate the following for low-lying Λ levels (small n): (i) The two-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 Λ level; and (ii) the three-body interaction for composite fermions is an order of magnitude smaller than the two-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low Λ levels, which is also supported by exact-diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors ν=n+ν2(n+ν)±1 and ν=n+1-ν2(n+1-ν)±1, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing Λ-level index, the two-body and three-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 ν=1/2.

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U2 - 10.1103/PhysRevB.96.245142

DO - 10.1103/PhysRevB.96.245142

M3 - Article

AN - SCOPUS:85040169287

VL - 96

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 2469-9950

IS - 24

M1 - 245142

ER -