We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters ($\ensuremath{\nu}$ and ${r}_{s}$ , respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large ${r}_{s}$ (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small ${r}_{s}$ . The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if ${r}_{s}>1$ . For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters ($\ensuremath{\nu}$ and ${r}_{s}$, respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large ${r}_{s}$ (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small ${r}_{s}$. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if ${r}_{s}>1$. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.

arXiv:cond-mat/0701219Physical Review BAug 3, 20077 citations

Local-spin-density functional for multideterminant density functional theory

Simone Paziani, Saverio Moroni, Paola Gori‐Giorgi +1 more

Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range Coulombic tail. This allows us to construct an analytic local-spin-density exchange-correlation functional appropriate to new, multideterminantal versions of the density functional theory, where quantum chemistry and approximate exchange-correlation functionals are combined to optimally describe both long- and short-range electron correlations.Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range Coulombic tail. This allows us to construct an analytic local-spin-density exchange-correlation functional appropriate to new, multideterminantal versions of the density functional theory, where quantum chemistry and approximate exchange-correlation functionals are combined to optimally describe both long- and short-range electron correlations.

arXiv:cond-mat/0601343Physical Review BApr 14, 2006126 citations

Spin correlations in a quasi-one-dimensional electron gas

B. Tanatar

Physica B Condensed MatterNov 1, 19968 citations

Effect of correlation on the properties of 2D spin-polarized dipolar Fermi gas

Rashmi Gangwar, Arup Banerjee, Amit Kumar Das

Abstract The spin-polarized 2D dipolar Fermi gas trapped in a harmonic potential provides an opportunity to study the many-fermion systems with strong particle–particle correlation in a controlled fashion. In this paper, we investigate the role of the correlation part of the interaction energy on the ground-state properties and on the collective oscillation frequencies of a 2D dipolar Fermi gas by employing density functional theory (DFT) within local density approximation. We employ a purely density-based, orbital-free approach of DFT to study the ground-state properties. We employ an orbital-free approach, as it is suitable for handling a large number of fermions (10 3 –10 4 atoms/molecules), which are typically the number of atoms/molecules contained in the samples of dipolar Fermi gas created in the laboratories. We derive analytical expressions for the frequencies of the monopole and quadrupole modes of the collective oscillations by employing a method based on the sum-rule approach of linear response theory. We find that the exchange and correlation part of the fermion–fermion interaction contributes significantly to the total energy, and their contributions increase with increasing number of fermions and interaction strength. In particular, the correlation part lowers the total energy of the 2D dipolar fermionic system, thereby stabilizing the system. Similarly, the inclusion of the correlation effect lowers the frequencies of the monopole mode of the collective oscillations appreciably in comparison to the case when this effect is not taken into account. On the other hand, the frequency of the quadrupole mode of the collective oscillations is not appreciably altered by the correlation part of the interaction over a wide range of values of interaction strength and number of fermions.Abstract The spin-polarized 2D dipolar Fermi gas trapped in a harmonic potential provides an opportunity to study the many-fermion systems with strong particle–particle correlation in a controlled fashion. In this paper, we investigate the role of the correlation part of the interaction energy on the ground-state properties and on the collective oscillation frequencies of a 2D dipolar Fermi gas by employing density functional theory (DFT) within local density approximation. We employ a purely density-based, orbital-free approach of DFT to study the ground-state properties. We employ an orbital-free approach, as it is suitable for handling a large number of fermions (10 3 –10 4 atoms/molecules), which are typically the number of atoms/molecules contained in the samples of dipolar Fermi gas created in the laboratories. We derive analytical expressions for the frequencies of the monopole and quadrupole modes of the collective oscillations by employing a method based on the sum-rule approach of linear response theory. We find that the exchange and correlation part of the fermion–fermion interaction contributes significantly to the total energy, and their contributions increase with increasing number of fermions and interaction strength. In particular, the correlation part lowers the total energy of the 2D dipolar fermionic system, thereby stabilizing the system. Similarly, the inclusion of the correlation effect lowers the frequencies of the monopole mode of the collective oscillations appreciably in comparison to the case when this effect is not taken into account. On the other hand, the frequency of the quadrupole mode of the collective oscillations is not appreciably altered by the correlation part of the interaction over a wide range of values of interaction strength and number of fermions.

Journal of Physics B Atomic Molecular and Optical PhysicsDec 6, 20194 citations

Exact relations for two-dimensional electron gas spin correlation functions

Ken-ichi Takiuchi, M. Okada, Hideki Koizumi +2 more

Physica E Low-dimensional Systems and NanostructuresFeb 1, 20003 citations

{r}_{s}

, respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large

{r}_{s}

(the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small

{r}_{s}

. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if

{r}_{s}>1

. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.