The fractional quantum Hall effect (FQHE) occurs at certain magnetic field strengths B*(n) in a two-dimensional electron gas of density n at strong magnetic fields perpendicular to the plane of the electron gas. At these magnetic fields strengths, the system is incompressible, i.e., there is a finite cost in energy for creating charge density fluctuations in the bulk, while the boundary of the electron gas has gapless modes of density waves. The bulk energy gap arises because of the strong electron-electron interactions. While there are very good models for infinite homogeneous systems and for the gapless excitations of the boundary of the electron gas, computational methods to accurately model finite, inhomogeneous systems with more then about ten electrons have not been available until very recently. We will here review an ensemble density functional approach to studying the ground state of large inhomogeneous spin polarized FQHE systems.The fractional quantum Hall effect (FQHE) occurs at certain magnetic field strengths B*(n) in a two-dimensional electron gas of density n at strong magnetic fields perpendicular to the plane of the electron gas. At these magnetic fields strengths, the system is incompressible, i.e., there is a finite cost in energy for creating charge density fluctuations in the bulk, while the boundary of the electron gas has gapless modes of density waves. The bulk energy gap arises because of the strong electron-electron interactions. While there are very good models for infinite homogeneous systems and for the gapless excitations of the boundary of the electron gas, computational methods to accurately model finite, inhomogeneous systems with more then about ten electrons have not been available until very recently. We will here review an ensemble density functional approach to studying the ground state of large inhomogeneous spin polarized FQHE systems.

arXiv:cond-mat/9603100Mar 14, 19960 citations

Description of exchange and correlation in the strongly inhomogeneous electron gas using a nonlocal density functional

Philip P. Rushton, David J. Tozer, Stewart J. Clark

We present exchange-correlation energy densities ${e}_{\mathrm{xc}},$ total energies ${E}_{\mathrm{xc}},$ and holes, calculated for strongly inhomogeneous electron gases using the nonlocal weighted density approximation. The results closely resemble variational Monte Carlo simulations performed recently [Phys. Rev. Lett. 87, 036401 (2001)], demonstrating the effectiveness of a nonlocal density functional description.We present exchange-correlation energy densities ${e}_{\mathrm{xc}},$ total energies ${E}_{\mathrm{xc}},$ and holes, calculated for strongly inhomogeneous electron gases using the nonlocal weighted density approximation. The results closely resemble variational Monte Carlo simulations performed recently [Phys. Rev. Lett. 87, 036401 (2001)], demonstrating the effectiveness of a nonlocal density functional description.

Physical review. B, Condensed matterMay 2, 200222 citations

On the low density regime of homogeneous electron gas

Tom Banks, Bingnan Zhang

arXiv:1909.00291Annals of PhysicsNov 4, 20191 citation

Aspects of Density Functional Approach to Many-Electron Systems

Swapan K. Ghosh

Lecture notes in chemistryJan 1, 19890 citations

We present exchange-correlation energy densities

{e}_{\mathrm{xc}},

total energies

{E}_{\mathrm{xc}},

and holes, calculated for strongly inhomogeneous electron gases using the nonlocal weighted density approximation. The results closely resemble variational Monte Carlo simulations performed recently [Phys. Rev. Lett. 87, 036401 (2001)], demonstrating the effectiveness of a nonlocal density functional description.