We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter $b$ $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter $b$ $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.

arXiv:cond-mat/0607130Physical Review BDec 22, 200691 citations

Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study

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

The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations. In the high-density regime ${(r}_{s}<~5)$ the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies similar to the released-node energies of Ceperley and Alder.The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations. In the high-density regime ${(r}_{s}<~5)$ the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies similar to the released-node energies of Ceperley and Alder.

arXiv:cond-mat/9803092Physical review. B, Condensed matterSep 15, 1998236 citations

Monte Carlo Studies of Many-Electron Systems

Robert L. Sugar

Springer proceedings in physicsJan 1, 19900 citations

Quantum Monte Carlo study of quasi-one-dimensional Bose gases

G. E. Astrakharchik, D Blume, S Giorgini +1 more

We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a 3D ; (iii) enters a unitary regime for | a 3D | → ∞ , where the properties of the gas are independent of a 3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a 3D ; (iii) enters a unitary regime for | a 3D | → ∞ , where the properties of the gas are independent of a 3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.

arXiv:cond-mat/0310749Journal of Physics B Atomic Molecular and Optical PhysicsMar 24, 200423 citations

Diffusion Monte Carlo study of strongly interacting 2D Fermi gases

Alexander Galea, Hillary Dawkins, Stefano Gandolfi +1 more

Nov 16, 20150 citations

b

$(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.

{(r}_{s}<~5)

the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies similar to the released-node energies of Ceperley and Alder.