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

Physical review. B, Condensed matter

Variational Monte Carlo calculation of the spin gap in the ν=1 quantum Hall liquid

Balázs Králik, Andrew M. Rappe, Steven G. Louie

Published Aug 15, 1997• 6 citations
Publisher

Abstract

A variational method of calculating the spin 1 excitation energies of the $\ensuremath{\nu}=1$ quantum Hall liquid is presented in detail. We are able to include Landau-level mixing and finite-thickness effects. The many-body wave functions of the states near $\ensuremath{\nu}=1$ filling are taken to be a product of a lowest-Landau-level Laughlin-type wave function and a Jastrow factor. A significant reduction in the calculated spin gap is found due both to Landau-level mixing $(\ensuremath{\sim}40%$ at ${r}_{s}=1)$ and to the effect of the finite thickness of the liquid (a further $\ensuremath{\sim}30%$ at ${r}_{s}=1)$. We find our calculations to be consistent with recent photoluminescence experiments in $\ensuremath{\delta}$-doped samples.

DOI
10.1103/physrevb.56.4760

Related papers

Various spin-polarization states beyond the maximum-density droplet: A quantum Monte Carlo study

Sami Siljamaki, Ari Harju, R. M. Nieminen +2 more

Using a variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy--state diagram of small quantum dots is studied in the magnetic-field range where the density of magnetic flux quanta just exceeds the density of electrons. An accurate analytical many-body wave function is constructed for various angular momentum and spin states in the lowest Landau level, and Landau-level mixing is then introduced using a Jastrow factor. The effect of higher Landau levels is shown to be significant; the transition lines are shifted considerably towards higher values of magnetic field and certain lowest-energy states vanish altogether.

arXiv:cond-mat/0112243•Physical review. B, Condensed matter•Mar 12, 2002•22 citations

Excitation gaps in fractional quantum Hall states: An exact diagonalization study

R. Morf, N. d’Ambrumenil, S. Das Sarma

We compute energy gaps for spin-polarized fractional quantum Hall states in the lowest Landau level (LL) at filling fractions $\ensuremath{\nu}=\frac{1}{3},$ $\frac{2}{5},$ $\frac{3}{7},$ and $\frac{4}{9}$ using exact diagonalization of systems with up to 16 particles and extrapolation to the infinite system-size limit. The gaps calculated for a pure Coulomb interaction and ignoring finite width effects, disorder and LL mixing agree well with the predictions of composite fermion theory provided the logarithmic corrections to the effective mass are included. This is in contrast with previous estimates, which, as we show, overestimated the gaps at $\ensuremath{\nu}=2/5$ and 3/7 by around 15%. We also study the reduction of the gaps as a result of the nonzero width of the two-dimensional (2D) layer. We show that these effects are accurately accounted for using either Gaussian or ``$z\ifmmode\times\else\texttimes\fi{}$ Gaussian'' $(z\mathrm{G})$ trial wave functions, which we show are significantly better variational wave functions than the Fang-Howard wave function. The Gaussian and $z\mathrm{G}$ wave functions give Haldane pseudopotential parameters which agree with those of self-consistent local density approximation calculations to better than $\ifmmode\pm\else\textpm\fi{}0.2%.$ For quantum well parameters typical of heterostructure samples, we find gap reductions of around 20%. The experimental gaps, after accounting heuristically for disorder, are still around 40% smaller than the computed gaps. However, for the case of tetracene layers in metal-insulator-semiconductor (MIS) devices we find that the measured activation gaps are close to those we compute. We discuss possible reasons why the difference between computed and measured activation gaps is larger in GaAs heterostructures than MIS devices. Finally, we present calculations using systems with up to 18 electrons of the gap at $\ensuremath{\nu}=\frac{5}{2}$ including width corrections.

arXiv:cond-mat/0202407•Physical review. B, Condensed matter•Aug 9, 2002•137 citations

Fractional quantum Hall liquid, Wigner solid phase boundary at finite density and magnetic field

Rodney Price, P. M. Platzman, Song He

At finite magnetic field and fixed filling factor \ensuremath{\nu}, as the particle density decreases, the fractional quantum Hall state will at some point give way to the Wigner solid. We calculate the ground-state energy of a Laughlin-like variational wave function at finite magnetic field and density by a quantum Monte Carlo method and compare the results with a calculation of the Wigner solid energy to get an estimate of the zero temperature finite density phase boundary.

Physical Review Letters•Jan 18, 1993•80 citations

Variational quantum Monte Carlo calculation of the effective spin Landégfactor in a two-dimensional electron system

Jung Hun Oh, K. J. Chang

We calculate the ground-state energy and the effective spin Land\'e g factor (${\mathit{g}}^{\mathrm{*}}$) of a two-dimensional electron gas in strong magnetic fields using a variational Monte Carlo method and many-body trial wave functions composed of the Jastrow correlation factor and the Laughlin-type functions. We find that ${\mathit{g}}^{\mathrm{*}}$ increases with decreasing of electron density and also shows increasing behavior as the filling factor \ensuremath{\nu} decreases in the region of 12. At \ensuremath{\nu}=1.0, ${\mathit{g}}^{\mathrm{*}}$ is estimated to be about 11 for a dimensionless parameter ${\mathit{r}}_{\mathit{s}}$=1.33, as compared to the measured value of 7.3, while considering impurity and phonon scatterings gives a better agreement of ${\mathit{g}}^{\mathrm{*}}$=9. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Aug 15, 1996•7 citations

Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas

Yongkyung Kwon, David M. Ceperley, Richard M. Martin

Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.

Physical review. B, Condensed matter•Jul 15, 1994•131 citations

Composite fermions and the energy gap in the fractional quantum Hall effect

N. E. Bonesteel

The energy gaps for the fractional quantum Hall effect at filling fractions 1/3, 1/5, and 1/7 have been calculated by variational Monte Carlo using Jain's composite-fermion wave functions. Results have been obtained before and after projection onto the lowest Landau level. The projected energy gaps agree well with exact-diagonalization results for small systems, lending support to the composite-fermion theory.

arXiv:cond-mat/9406110•Physical review. B, Condensed matter•Apr 15, 1995•18 citations
A variational method of calculating the spin 1 excitation energies of the \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=1 quantum Hall liquid is presented in detail. We are able to include Landau-level mixing and finite-thickness effects. The many-body wave functions of the states near \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=1 filling are taken to be a product of a lowest-Landau-level Laughlin-type wave function and a Jastrow factor. A significant reduction in the calculated spin gap is found due both to Landau-level mixing (\ensuremath∼40(\ensuremath{\sim}40%(\ensuremath∼40 at rs=1){r}_{s}=1)rs​=1) and to the effect of the finite thickness of the liquid (a further \ensuremath∼30\ensuremath{\sim}30%\ensuremath∼30 at rs=1){r}_{s}=1)rs​=1). We find our calculations to be consistent with recent photoluminescence experiments in \ensuremathδ\ensuremath{\delta}\ensuremathδ-doped samples.
Using a variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy--state diagram of small quantum dots is studied in the magnetic-field range where the density of magnetic flux quanta just exceeds the density of electrons. An accurate analytical many-body wave function is constructed for various angular momentum and spin states in the lowest Landau level, and Landau-level mixing is then introduced using a Jastrow factor. The effect of higher Landau levels is shown to be significant; the transition lines are shifted considerably towards higher values of magnetic field and certain lowest-energy states vanish altogether.
We compute energy gaps for spin-polarized fractional quantum Hall states in the lowest Landau level (LL) at filling fractions $\ensuremath{\nu}=\frac{1}{3},$ 25,\frac{2}{5},52​, 37,\frac{3}{7},73​, and 49\frac{4}{9}94​ using exact diagonalization of systems with up to 16 particles and extrapolation to the infinite system-size limit. The gaps calculated for a pure Coulomb interaction and ignoring finite width effects, disorder and LL mixing agree well with the predictions of composite fermion theory provided the logarithmic corrections to the effective mass are included. This is in contrast with previous estimates, which, as we show, overestimated the gaps at $\ensuremath{\nu}=2/5$ and 3/7 by around 15%. We also study the reduction of the gaps as a result of the nonzero width of the two-dimensional (2D) layer. We show that these effects are accurately accounted for using either Gaussian or ``$z\ifmmode\times\else\texttimes\fi{}$ Gaussian'' (zG)(z\mathrm{G})(zG) trial wave functions, which we show are significantly better variational wave functions than the Fang-Howard wave function. The Gaussian and zGz\mathrm{G}zG wave functions give Haldane pseudopotential parameters which agree with those of self-consistent local density approximation calculations to better than $\ifmmode\pm\else\textpm\fi{}0.2%.$ For quantum well parameters typical of heterostructure samples, we find gap reductions of around 20%. The experimental gaps, after accounting heuristically for disorder, are still around 40% smaller than the computed gaps. However, for the case of tetracene layers in metal-insulator-semiconductor (MIS) devices we find that the measured activation gaps are close to those we compute. We discuss possible reasons why the difference between computed and measured activation gaps is larger in GaAs heterostructures than MIS devices. Finally, we present calculations using systems with up to 18 electrons of the gap at $\ensuremath{\nu}=\frac{5}{2}$ including width corrections.
We calculate the ground-state energy and the effective spin Land\'e g factor (g∗{\mathit{g}}^{\mathrm{*}}g∗) of a two-dimensional electron gas in strong magnetic fields using a variational Monte Carlo method and many-body trial wave functions composed of the Jastrow correlation factor and the Laughlin-type functions. We find that g∗{\mathit{g}}^{\mathrm{*}}g∗ increases with decreasing of electron density and also shows increasing behavior as the filling factor \ensuremath{\nu} decreases in the region of 12. At \ensuremath{\nu}=1.0, g∗{\mathit{g}}^{\mathrm{*}}g∗ is estimated to be about 11 for a dimensionless parameter rs{\mathit{r}}_{\mathit{s}}rs​=1.33, as compared to the measured value of 7.3, while considering impurity and phonon scatterings gives a better agreement of g∗{\mathit{g}}^{\mathrm{*}}g∗=9. \textcopyright{} 1996 The American Physical Society.
Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.