New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular momentum for each pair, and then making the paired quasielectrons condense into a 1/4 Laughlin state. The quasiparticle excitations of the proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian fractional statistics. In the spherical geometry, the total flux quanta $N_ϕ$ is shown to be related to the number of electrons $N$ by $N_ϕ = 2N-(5-q)$ with $q$ being the relative angular momentum between the quasielectrons in each pair which takes values of non-negative even integers. The overlaps are calculated between the proposed trial wave functions, including the ground state, quasiexciton states, and quasihole states, and the exact states of the finite size systems at $N_ϕ = 2N-3$ . The near unity overlaps are obtained in the lowest Landau level, while the moderate overlaps are obtained in the second Landau level. The relevance of the wave functions to the yet to be discovered fractional quantum Hall effect in the lowest Landau level, as well as the 5/2 quantum Hall effect is also discussed.New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular momentum for each pair, and then making the paired quasielectrons condense into a 1/4 Laughlin state. The quasiparticle excitations of the proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian fractional statistics. In the spherical geometry, the total flux quanta $N_ϕ$ is shown to be related to the number of electrons $N$ by $N_ϕ = 2N-(5-q)$ with $q$ being the relative angular momentum between the quasielectrons in each pair which takes values of non-negative even integers. The overlaps are calculated between the proposed trial wave functions, including the ground state, quasiexciton states, and quasihole states, and the exact states of the finite size systems at $N_ϕ = 2N-3$. The near unity overlaps are obtained in the lowest Landau level, while the moderate overlaps are obtained in the second Landau level. The relevance of the wave functions to the yet to be discovered fractional quantum Hall effect in the lowest Landau level, as well as the 5/2 quantum Hall effect is also discussed.

arXiv:1112.4650Dec 20, 20110 citations

Quantum Hall Gas around Half-filled Landau Level

展希前田, 哲行落合, 健三石川

素粒子論研究May 20, 19990 citations

‘One-dimensional’ theory of the quantum Hall system

Emil J. Bergholtz, A. Karlhede

We consider the lowest Landau level on a torus as a function of its circumference L 1 . When L 1 → 0, the ground state at general rational filling fraction is a crystal with a gap—a Tao–Thouless state. For filling fractions ν = p /(2 pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L 1 → ∞ . For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral fermions (dipoles), or rather to a Luttinger liquid modification thereof, at L 1 ∼ 5 magnetic lengths. Using exact diagonalization we identify this state as a version of the Rezayi–Read state, and find that it develops continuously into the state that is believed to describe the observed metallic phase as L 1 → ∞ . Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.We consider the lowest Landau level on a torus as a function of its circumference L 1 . When L 1 → 0, the ground state at general rational filling fraction is a crystal with a gap—a Tao–Thouless state. For filling fractions ν = p /(2 pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L 1 → ∞ . For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral fermions (dipoles), or rather to a Luttinger liquid modification thereof, at L 1 ∼ 5 magnetic lengths. Using exact diagonalization we identify this state as a version of the Rezayi–Read state, and find that it develops continuously into the state that is believed to describe the observed metallic phase as L 1 → ∞ . Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.

arXiv:cond-mat/0509434Journal of Statistical Mechanics Theory and ExperimentApr 12, 200688 citations

Trial Wavefunctions and Ground State Energies of Some Non-Laughlin Correlated Quantum Hall Systems

John J. Quinn

APSMar 1, 20110 citations

Quantum Hall States in Rotating Spin-1 Bose Systems

N. Read

APSMar 1, 20030 citations

Role of reversed spins in the correlated ground state for the fractional quantum Hall effect

Tapash Chakraborty, Fu‐Chun Zhang

The ground-state energy for the correlated liquid state of Laughlin with one-half of the electrons having spins antiparallel to the field is obtained at $\frac{2}{5}$ filling of the lowest Landau level. The energy is found to be lower compared with the potential energy of the spin-polarized state. The energy difference is small, however, compared with the difference of magnetic energies between the two states under the present experimental conditions. Some of the results obtained for the one-spin state are in good agreement with recent experimental observations and very accurate Monte Carlo results.The ground-state energy for the correlated liquid state of Laughlin with one-half of the electrons having spins antiparallel to the field is obtained at $\frac{2}{5}$ filling of the lowest Landau level. The energy is found to be lower compared with the potential energy of the spin-polarized state. The energy difference is small, however, compared with the difference of magnetic energies between the two states under the present experimental conditions. Some of the results obtained for the one-spin state are in good agreement with recent experimental observations and very accurate Monte Carlo results.

Physical review. B, Condensed matterJun 15, 1984106 citations

\pm1/4

of electron charge, and obey Abelian fractional statistics. In the spherical geometry, the total flux quanta

N_ϕ

is shown to be related to the number of electrons

N

N_ϕ = 2N-(5-q)

with

q

being the relative angular momentum between the quasielectrons in each pair which takes values of non-negative even integers. The overlaps are calculated between the proposed trial wave functions, including the ground state, quasiexciton states, and quasihole states, and the exact states of the finite size systems at

N_ϕ = 2N-3

. The near unity overlaps are obtained in the lowest Landau level, while the moderate overlaps are obtained in the second Landau level. The relevance of the wave functions to the yet to be discovered fractional quantum Hall effect in the lowest Landau level, as well as the 5/2 quantum Hall effect is also discussed.

The ground-state energy for the correlated liquid state of Laughlin with one-half of the electrons having spins antiparallel to the field is obtained at

\frac{2}{5}

filling of the lowest Landau level. The energy is found to be lower compared with the potential energy of the spin-polarized state. The energy difference is small, however, compared with the difference of magnetic energies between the two states under the present experimental conditions. Some of the results obtained for the one-spin state are in good agreement with recent experimental observations and very accurate Monte Carlo results.