For a finite number of electrons confined to a spherical surface, Jain's composite fermion (CF) picture gives a unique relationship between the value of the degeneracy, ${\mathit{N}}_{\mathit{L}}$ =2S+1, of the lowest electron shell and the number of electrons for which a given incompressible quantum-liquid state of filling factor \ensuremath{\nu} occurs. For states close to the Laughlin \ensuremath{\nu}=1/3 state, two different mean-field CF descriptions can be applied. Some insight into quasielectron-quasihole symmetry and the nature of the lowest-energy sector of the energy spectrum can be obtained by comparing the different mean-field CF pictures. \textcopyright{} 1996 The American Physical Society.For a finite number of electrons confined to a spherical surface, Jain's composite fermion (CF) picture gives a unique relationship between the value of the degeneracy, ${\mathit{N}}_{\mathit{L}}$=2S+1, of the lowest electron shell and the number of electrons for which a given incompressible quantum-liquid state of filling factor \ensuremath{\nu} occurs. For states close to the Laughlin \ensuremath{\nu}=1/3 state, two different mean-field CF descriptions can be applied. Some insight into quasielectron-quasihole symmetry and the nature of the lowest-energy sector of the energy spectrum can be obtained by comparing the different mean-field CF pictures. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterDec 15, 19963 citations

Second Generation of Composite Fermions

M. O. Goerbig, Pascal Lederer, C. Morais Smith

arXiv:cond-mat/0308021Aug 1, 20030 citations

Theory and Applications of Composite Fermion Edge States

HS Sim, G. Ihm, Kee-Joo Chang

Jan 1, 19990 citations

s -Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1

Glenn Wagner, Dung X. Nguyen, Steven H. Simon +1 more

We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The s-wave trial wave function naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The s-wave trial wave function naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.

arXiv:2106.00690Physical Review LettersDec 10, 202121 citations

Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions

Cristian Voinea, Songyang Pu, Ajit Coimbatore Balram +1 more

The composite fermion Fermi liquid (CFL) state at ν = 1 / 2 filling of a Landau level is a paradigmatic non-Fermi liquid borne out purely by Coulomb interactions. But in what ways is this exotic state of matter different from a Fermi liquid? The CFL entanglement entropy was indeed found to exhibit a significant enhancement compared to free electrons [J. Shao , ], which was subsequently ruled out as a finite-size effect by the study of a lattice CFL analog [R. V. Mishmash and O. I. Motrunich, ]. Moreover, the enhancement was not observed in a quasi-one-dimensional limit of the Coulomb ground state at ν = 1 / 2 [S. D. Geraedts , ]. Here, we revisit the problem of entanglement scaling in the CFL state realized in a two-dimensional electron gas. Using Monte Carlo evaluation of the second Rényi entropy S 2 for the CFL variational wave function, we show that the entanglement enhancement is present not only at ν = 1 / 2 , but also at ν = 1 / 4 , as well as in bosonic CFL states at ν = 1 and ν = 1 / 3 fillings. In all cases, we find the scaling of S 2 with subsystem size to be enhanced compared to the noninteracting case, and insensitive to the choice of geometry and projection to the lowest Landau level. We also demonstrate that for CFL states, the variance of the particle number in a subsystem obeys area-law scaling with a universal subleading corner contribution, in stark contrast with free fermions. Our results establish the enhanced entanglement scaling and suppressed charge fluctuations as fingerprints of non-Fermi-liquid correlations in CFL states.The composite fermion Fermi liquid (CFL) state at ν = 1 / 2 filling of a Landau level is a paradigmatic non-Fermi liquid borne out purely by Coulomb interactions. But in what ways is this exotic state of matter different from a Fermi liquid? The CFL entanglement entropy was indeed found to exhibit a significant enhancement compared to free electrons [J. Shao , ], which was subsequently ruled out as a finite-size effect by the study of a lattice CFL analog [R. V. Mishmash and O. I. Motrunich, ]. Moreover, the enhancement was not observed in a quasi-one-dimensional limit of the Coulomb ground state at ν = 1 / 2 [S. D. Geraedts , ]. Here, we revisit the problem of entanglement scaling in the CFL state realized in a two-dimensional electron gas. Using Monte Carlo evaluation of the second Rényi entropy S 2 for the CFL variational wave function, we show that the entanglement enhancement is present not only at ν = 1 / 2 , but also at ν = 1 / 4 , as well as in bosonic CFL states at ν = 1 and ν = 1 / 3 fillings. In all cases, we find the scaling of S 2 with subsystem size to be enhanced compared to the noninteracting case, and insensitive to the choice of geometry and projection to the lowest Landau level. We also demonstrate that for CFL states, the variance of the particle number in a subsystem obeys area-law scaling with a universal subleading corner contribution, in stark contrast with free fermions. Our results establish the enhanced entanglement scaling and suppressed charge fluctuations as fingerprints of non-Fermi-liquid correlations in CFL states.

arXiv:2407.11119Physical review. B./Physical review. BMar 6, 20254 citations

Interacting Composite Fermions

Chia‐Chen Chang

Jun 22, 20060 citations

For a finite number of electrons confined to a spherical surface, Jain's composite fermion (CF) picture gives a unique relationship between the value of the degeneracy,

{\mathit{N}}_{\mathit{L}}

=2S+1, of the lowest electron shell and the number of electrons for which a given incompressible quantum-liquid state of filling factor \ensuremath{\nu} occurs. For states close to the Laughlin \ensuremath{\nu}=1/3 state, two different mean-field CF descriptions can be applied. Some insight into quasielectron-quasihole symmetry and the nature of the lowest-energy sector of the energy spectrum can be obtained by comparing the different mean-field CF pictures. \textcopyright{} 1996 The American Physical Society.