Europhysics Letters (EPL)

A new hypernetted-chain treatment for Laughlin quantum Hall states

Orion Ciftja, Stefano Fantoni

Published Dec 20, 1996• 17 citations

Abstract

The hypernetted-chain theory is applied to study the fractional quantum Hall effect with the Laughlin wave functions. A new method is proposed to include the effect of the elementary diagrams, which improves upon the commonly used modified hypernetted-chain approximation. The correlation energy, the pair distribution function, as well as the magnetoroton excitation spectrum have been computed within this method. The results obtained are in very good agreement with the available Monte Carlo estimates. The method is generalizable to treat other wave functions, like those corresponding to the hierarchical states or those of composite fermion type.

DOI: 10.1209/epl/i1996-00284-x

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Europhysics Letters (EPL)

A new hypernetted-chain treatment for Laughlin quantum Hall states

Orion Ciftja, Stefano Fantoni

Published Dec 20, 1996• 17 citations

Publisher

Abstract

DOI: 10.1209/epl/i1996-00284-x

Related papers

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Hypernetted-chain approximation and quasiparticle energies in the (1/3 fractional quantized Hall effect

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J. W. Kim, H. Kim, N. Kim

We apply Fermi hypernetted-chain theory to study the spin polarization of higher-order fractional quantum Hall (FQH) states at filling factors in between the primary FQH sequences, $\ensuremath{\nu}=p/({q}_{e}p\ifmmode\pm\else\textpm\fi{}1)$, where ${q}_{e}$ is an even integer and $p$ is a nonzero integer. The filling factors related to the higher-order FQH states include $\ensuremath{\nu}=3/8$, $4/11$ , $5/13$ , $5/17$ , $4/13$ , $6/17$ , $7/11$ , and so on. We use a model of strongly interacting fermions with different spin degrees of freedom to explain the states beyond primary FQH sequences. We calculate the correlation energy, the radial distribution function, as well as the static structure function associated with the Halperin wave function adopted for the mixture states of fermions with different spins. The results are comparable with those from the residual interaction between composite fermions.We apply Fermi hypernetted-chain theory to study the spin polarization of higher-order fractional quantum Hall (FQH) states at filling factors in between the primary FQH sequences, $\ensuremath{\nu}=p/({q}_{e}p\ifmmode\pm\else\textpm\fi{}1)$, where ${q}_{e}$ is an even integer and $p$ is a nonzero integer. The filling factors related to the higher-order FQH states include $\ensuremath{\nu}=3/8$, $4/11$, $5/13$, $5/17$, $4/13$, $6/17$, $7/11$, and so on. We use a model of strongly interacting fermions with different spin degrees of freedom to explain the states beyond primary FQH sequences. We calculate the correlation energy, the radial distribution function, as well as the static structure function associated with the Halperin wave function adopted for the mixture states of fermions with different spins. The results are comparable with those from the residual interaction between composite fermions.

Physical review. B./Physical review. BApr 6, 20170 citations

{g}_{112}

of a classical plasma with two particle species. We apply this approximation to the Laughlin trial wave functions for the case \ensuremath{\nu}=(1/3 and we estimate their energies. Our quasihole energy is in good agreement with past calculations, but our quasielectron energy is considerably higher than the accepted result. However, the approximation has the correct property that near a quasielectron, the electron pair correlation function vanishes as \ensuremath{\Vert}

{\mathrm{r}}_{1}

${\mathrm{\ensuremath{-}}\mathrm{r}}_{2}$${\ensuremath{\Vert}}^{2}$ for \ensuremath{\Vert}

{\mathrm{r}}_{1}

${\mathrm{\ensuremath{-}}\mathrm{r}}_{2}$\ensuremath{\Vert}\ensuremath{\rightarrow}0, where

{\mathrm{r}}_{1}

and

{\mathrm{r}}_{2}

are electron positions. We show that an approximation analogous to Laughlin's pseudopotential approximation does not have this property.

{q}_{e}

is an even integer and

p

is a nonzero integer. The filling factors related to the higher-order FQH states include $\ensuremath{\nu}=3/8$,

4/11

5/13

5/17

4/13

6/17

7/11

, and so on. We use a model of strongly interacting fermions with different spin degrees of freedom to explain the states beyond primary FQH sequences. We calculate the correlation energy, the radial distribution function, as well as the static structure function associated with the Halperin wave function adopted for the mixture states of fermions with different spins. The results are comparable with those from the residual interaction between composite fermions.