Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Condensed Matter

Finite-size scaling studies of 2D electrons at half-filling

S. T. Chui, Timothy A. L. Ziman

Published May 10, 1993• 1 citation
Publisher

Abstract

Finite-size exact diagonalization of the Hamiltonian for four, eight and 16 electrons in a half-filled Landau level under periodic boundary conditions in a rectangular geometry was carried out. The magnitude of the peak value of the structure factor is found to increase with the system size to the power 0.36, consistent with a picture of a quasi-solid discussed by Chui. The energy difference of the lowest-energy state of the two different particle-hole symmetry manifolds decreases as the system size is increased, suggestive of broken particle-hole symmetry.

DOI
10.1088/0953-8984/5/19/003

Related papers

TWO-DIMENSIONAL TWO LAYER ELECTRONS NEAR A HALF-FILLED LANDAU LEVEL

S. T. Chui

We report finite cluster exact diagonalization studies under periodic boundary conditions of two layers of electrons in a strong magnetic field at a half-filled Landau level. For the system studied by Suen et al., the ground states have more than 97 per cent of its spectral weight in the symmetric single particle levels. The eigenfunctions and eigenvalues up to a constant factor for different aspect ratios are essentially the same as previous numerical results of a single layer of electrons of zero thickness at half-filling.

Modern Physics Letters B•Nov 20, 1992•0 citations

Charge-Density-Wave Ordering in Half-Filled High Landau Levels

Edward H. Rezayi, F. D. M. Haldane, Kun Yang

We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level (index $N\ensuremath{\ge}2$) half filled by electrons. Strong and sharp peaks are found in the wave-vector dependence of both the static density susceptibility and the equal-time density-density correlation function, in finite-size systems with up to twelve electrons. Qualitatively different from the partially filled lowest ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) Landau level, these results are suggestive of a tendency toward charge-density-wave ordering in these systems. The ordering wave vector is found to decrease with increasing $N$.

arXiv:cond-mat/9903258•Physical Review Letters•Aug 9, 1999•140 citations

Wigner solid from finite-cluster studies

S. T. Chui, Xiu Qiu

We perform finite-cluster exact diagonalization studies for electrons in the lowest Landau level for filling factors from 1/3 to 1/11. In contrast to previous studies, we focus on the ground-state eigenfunction. This wave function changes continuously for filling factors from 1/3 to 1/9. At a filling factor of 1/11, there is a dramatic qualitative change in the ground-state wave function. Associated with this change is a peak in the structure factor at a finite wave vector as well as excitation energies that are consistent with gapless excitations at 1/11 filling. These results are consistent with recent experimental findings.

Physical review. B, Condensed matter•Jun 15, 1991•4 citations

Renormalization-group calculation for electrons in a half-filled Landau level

S. T. Chui

The major obstacle for analytic calculations for electrons in the lowest Landau level arises from the degeneracy of the single-particle eigenstates. When the electron-electron interaction is included, the diagonal energy of different basis states is no longer the same and degenerate perturbation theory can be carried out. The near degeneracy of the single-particle states is manifested as an infrared-divergent perturbation series which is similar to that of a collection of one-dimensional interacting spinless chains. Thus a renormalization-group scheme can be developed. The range of the interparticle potential affects the change in diagonal energy for particle-hole fluctuations. For the Coulomb potential we find that the coupling constants remain unchanged over many length scales. The system remains gapless, consistent with recent transport and surface-acoustic-wave measurements.

Physical review. B, Condensed matter•Dec 15, 1993•1 citation

Ising Ferromagnetism of Composite Fermions

Karel Výborný, Ondřej Čertı́k, Daniela Pfannkuche +3 more

The quantum Hall ferromagnets at the half-filling of a pair of degenerate electron or composite fermion Landau levels are studied by exact numerical diagonalization.The results obtained using open and closed geometries (rectangular -with periodic boundary conditions and spherical) are compared.The ferro-and paramagnetic ground states are identified in finite-size energy spectra, and the pair-correlation functions are used in search of the domain structure at half-polarization.

Acta Physica Polonica A•Sep 1, 2006•3 citations

Finite-size Monte Carlo results for anisotropic quantum Hall liquids

Orion Ciftja, Brittney Cornelius, Kesha Brown +1 more

At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit remarkable quantum phenomena. In these extreme conditions, strongly correlated electron systems stabilize in different quantum phases as the filling factor of Landau levels is varied. In this Brief Report we present finite-size Monte Carlo simulation results for anisotropic quantum Hall liquid states observed at certain even-denominator filling factors. The anisotropic electronic liquid phases are described by a broken rotational symmetry wave function. Our investigations of systems of few electrons in disk geometry indicate that an anisotropic liquid-crystalline quantum Hall phase with broken rotational symmetry is energetically favored relative to an isotropic liquid one.

Physical Review B•May 5, 2011•12 citations
Finite-size exact diagonalization of the Hamiltonian for four, eight and 16 electrons in a half-filled Landau level under periodic boundary conditions in a rectangular geometry was carried out. The magnitude of the peak value of the structure factor is found to increase with the system size to the power 0.36, consistent with a picture of a quasi-solid discussed by Chui. The energy difference of the lowest-energy state of the two different particle-hole symmetry manifolds decreases as the system size is increased, suggestive of broken particle-hole symmetry.
We report finite cluster exact diagonalization studies under periodic boundary conditions of two layers of electrons in a strong magnetic field at a half-filled Landau level. For the system studied by Suen et al., the ground states have more than 97 per cent of its spectral weight in the symmetric single particle levels. The eigenfunctions and eigenvalues up to a constant factor for different aspect ratios are essentially the same as previous numerical results of a single layer of electrons of zero thickness at half-filling.
We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level (index $N\ensuremath{\ge}2$) half filled by electrons. Strong and sharp peaks are found in the wave-vector dependence of both the static density susceptibility and the equal-time density-density correlation function, in finite-size systems with up to twelve electrons. Qualitatively different from the partially filled lowest ( N=0N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0N=0) Landau level, these results are suggestive of a tendency toward charge-density-wave ordering in these systems. The ordering wave vector is found to decrease with increasing NNN.
We perform finite-cluster exact diagonalization studies for electrons in the lowest Landau level for filling factors from 1/3 to 1/11. In contrast to previous studies, we focus on the ground-state eigenfunction. This wave function changes continuously for filling factors from 1/3 to 1/9. At a filling factor of 1/11, there is a dramatic qualitative change in the ground-state wave function. Associated with this change is a peak in the structure factor at a finite wave vector as well as excitation energies that are consistent with gapless excitations at 1/11 filling. These results are consistent with recent experimental findings.
The major obstacle for analytic calculations for electrons in the lowest Landau level arises from the degeneracy of the single-particle eigenstates. When the electron-electron interaction is included, the diagonal energy of different basis states is no longer the same and degenerate perturbation theory can be carried out. The near degeneracy of the single-particle states is manifested as an infrared-divergent perturbation series which is similar to that of a collection of one-dimensional interacting spinless chains. Thus a renormalization-group scheme can be developed. The range of the interparticle potential affects the change in diagonal energy for particle-hole fluctuations. For the Coulomb potential we find that the coupling constants remain unchanged over many length scales. The system remains gapless, consistent with recent transport and surface-acoustic-wave measurements.
At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit remarkable quantum phenomena. In these extreme conditions, strongly correlated electron systems stabilize in different quantum phases as the filling factor of Landau levels is varied. In this Brief Report we present finite-size Monte Carlo simulation results for anisotropic quantum Hall liquid states observed at certain even-denominator filling factors. The anisotropic electronic liquid phases are described by a broken rotational symmetry wave function. Our investigations of systems of few electrons in disk geometry indicate that an anisotropic liquid-crystalline quantum Hall phase with broken rotational symmetry is energetically favored relative to an isotropic liquid one.