arXiv:cond-mat/0304517

Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder

Emil J. Bergholtz, A. Karlhede

Published Apr 23, 2003• 3 citations

Abstract

We investigate the ground state properties of a two-dimensional electron gas in the lowest Landau level using the Density Matrix Renormalization Group. The electron gas is confined to a cylinder with a strong magnetic field perpendicular to the surface. For a thin cylinder, the ground state is for generic filling factors a charge density wave state, however, at $ν=1/2$ a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.

DOI: 10.48550/arxiv.cond-mat/0304517

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arXiv:cond-mat/0304517

Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder

Emil J. Bergholtz, A. Karlhede

Published Apr 23, 2003• 3 citations

arXiv HTML PDF

Abstract

ν=1/2

a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.

DOI: 10.48550/arxiv.cond-mat/0304517

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Naokazu Shibata, D. Yoshioka

arXiv:cond-mat/0311213Journal of the Physical Society of JapanJan 15, 200415 citations

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Prashant Kumar, F. D. M. Haldane

We use the dynamical structure factors of the quantum Hall states at $\ensuremath{\nu}=1/3$ and $1/2$ in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low-energy properties. At $\ensuremath{\nu}=1/3$, a sharp magnetoroton mode and the two-roton continuum are present and the finite-size effects can be understood using the fractional charge of the quasiparticle. At $\ensuremath{\nu}=1/2$, we find low-energy modes with linear dispersion and the static structure factor $\overline{s}(q)\ensuremath{\sim}{(q\ensuremath{\ell})}^{3}$ in the limit $q\ensuremath{\ell}\ensuremath{\rightarrow}0$. The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.We use the dynamical structure factors of the quantum Hall states at $\ensuremath{\nu}=1/3$ and $1/2$ in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low-energy properties. At $\ensuremath{\nu}=1/3$, a sharp magnetoroton mode and the two-roton continuum are present and the finite-size effects can be understood using the fractional charge of the quasiparticle. At $\ensuremath{\nu}=1/2$, we find low-energy modes with linear dispersion and the static structure factor $\overline{s}(q)\ensuremath{\sim}{(q\ensuremath{\ell})}^{3}$ in the limit $q\ensuremath{\ell}\ensuremath{\rightarrow}0$. The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.

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Physical review. B, Condensed matterDec 15, 19931 citation

ν=1/2

a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.

We use the dynamical structure factors of the quantum Hall states at $\ensuremath{\nu}=1/3$ and

1/2

in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low-energy properties. At $\ensuremath{\nu}=1/3$, a sharp magnetoroton mode and the two-roton continuum are present and the finite-size effects can be understood using the fractional charge of the quasiparticle. At $\ensuremath{\nu}=1/2$, we find low-energy modes with linear dispersion and the static structure factor $\overline{s}(q)\ensuremath{\sim}{(q\ensuremath{\ell})}^{3}$ in the limit $q\ensuremath{\ell}\ensuremath{\rightarrow}0$. The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.

The ground-state phase diagram of 2D electrons in a high Landau level (index

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to

1/2

. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.