Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0811.0725 · Journal of Physics A Mathematical and Theoretical

Spin resolved energy parametrization of a quasi-one-dimensional electron gas

Luke Shulenburger, Michele Casula, Gaetano Senatore, Richard M. Martin

Published May 8, 2009• 15 citations
arXivHTMLPDF

Abstract

By carrying out extensive lattice regularized diffusion Monte Carlo calculations, we study the spin and density dependence of the ground-state energy for a quasi-one-dimensional electron gas, with harmonic transverse confinement and long-range 1/ r interactions. We present a parametrization of the exchange–correlation energy suitable for spin density functional calculations, which fulfils exact low and high density limits.

DOI
10.1088/1751-8113/42/21/214021

Related papers

Ground state properties of the one-dimensional Coulomb gas using the lattice regularized diffusion Monte Carlo method

Michele Casula, Sandro Sorella, Gaetano Senatore

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/0607130•Physical Review B•Dec 22, 2006•91 citations

Correlation energy of the paramagnetic electron gas at the thermodynamic limit

Sam Azadi, N. D. Drummond, Sam M. Vinko

The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground-state energies in finite cells are determined using Slater-Jastrow-backflow trial wave functions, and finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Our correlation energies in the thermodynamic limit are more accurate than previous results. The present diffusion quantum Monte Carlo energies together with our recently reported [Phys. Rev. B 105, 245135 (2022)] results at low density, are used to parametrize the correlation energy of the electron gas using a functional form that satisfies the exact asymptotic behavior at high density.

arXiv:2209.10227•Physical review. B./Physical review. B•Mar 15, 2023•9 citations

Excitation spectrum of the quasi-one-dimensional electron gas with long-range Coulomb interaction

Alfred Gold, L. Calmels

Using ground-state energy calculations we calculate the density and width dependence of the spin susceptibility and the compressibility of the one-dimensional electron gas with long-range Coulomb interaction. An oscillator potential is used for the confinement. With the compressibility and the spin-susceptibility sum rule we describe charge-density and spin-density excitations in quantum wires as a function of the electron density and the wire-width parameter. Analytical results are presented.

Physical review. B, Condensed matter•Aug 15, 1998•11 citations

Correlation effects in one-dimensional metallic quantum wires under various confinements

Vidit Gangwar, Vinod Ashokan, Ankush Girdhar +3 more

Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths b and density parameters r s . In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground-state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of b and r s . Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire ( b → 0 ) in the high-density limit, we find that the correlation energy for transverse confinement models V 1 ( q ) (harmonic), V 2 ( q ) (cylindrical), and V 5 ( q ) (harmonic-delta) approaches ε c ( r s ) = − π 2 / 360 ∼ − 0.02741 a.u., which agrees with the exact results in this limit [P.-F. Loos, ; V. Ashokan, , ]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance x = 0 to yield the same correlation energy. In contrast, other confinement potentials, V 3 ( q ) (infinite square well), V 4 ( q ) (infinite square-infinite triangular well), and V 6 ( q ) (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to ε c ∼ − 0.03002 a.u. for these potentials. The percentage difference in correlation energy between the confinement models V 1 ( q ) , V 2 ( q ) , V 5 ( q ) and V 3 ( q ) ,

arXiv:2507.17925•Physical review. B./Physical review. B•Dec 9, 2025•2 citations

Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density

Ankush Girdhar, Vinod Ashokan, N. D. Drummond +2 more

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths $b$ and density parameters ${r}_{\text{s}}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density. It is observed that the peak in the static structure factor at $k=2{k}_{\text{F}}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter ${K}_{\ensuremath{\rho}}$ from the momentum density. It is found that ${K}_{\ensuremath{\rho}}$ increases by about 10% between wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of finite-thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b\ensuremath{\ll}{r}_{\text{s}}<1$. It is found that the correlation energy varies as ${b}^{2}$ for $b\ensuremath{\ll}{r}_{\text{s}}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of $b$ and ${r}_{\text{s}}\ensuremath{\le}1$. These are compared with the QMC results in the range of applicability of the theory.

arXiv:2112.12064•Physical review. B./Physical review. B•Mar 30, 2022•9 citations

Spin-susceptibility and spin-density excitations of the quasi-one-dimensional interacting electron gas: many-body effects for cylindrical confinement

Alfred Gold, L. Calmels

We calculate the ground-state energy of a quasi-one-dimensional electron gas with Coulomb interaction depending on the spin-polarization parameter and the Wigner-Seitz parameter . Cylindrical quantum wires of radius are considered. We describe the pair-correlation function g(z = 0) as a function of and . We derive the spin-susceptibility as a function of and in different approximations. Numerical results obtained for the spin-susceptibility are fitted by an analytical expression. Collective modes (charge-density and spin-density excitations) in cylindrical quantum wires are described and the validity range of our calculation is discussed.

Journal of Physics Condensed Matter•Jun 1, 1998•3 citations
By carrying out extensive lattice regularized diffusion Monte Carlo calculations, we study the spin and density dependence of the ground-state energy for a quasi-one-dimensional electron gas, with harmonic transverse confinement and long-range 1/ r interactions. We present a parametrization of the exchange–correlation energy suitable for spin density functional calculations, which fulfils exact low and high density limits.
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 bbb $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, 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.
The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground-state energies in finite cells are determined using Slater-Jastrow-backflow trial wave functions, and finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Our correlation energies in the thermodynamic limit are more accurate than previous results. The present diffusion quantum Monte Carlo energies together with our recently reported [Phys. Rev. B 105, 245135 (2022)] results at low density, are used to parametrize the correlation energy of the electron gas using a functional form that satisfies the exact asymptotic behavior at high density.
Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths b and density parameters r s . In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground-state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of b and r s . Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire ( b → 0 ) in the high-density limit, we find that the correlation energy for transverse confinement models V 1 ( q ) (harmonic), V 2 ( q ) (cylindrical), and V 5 ( q ) (harmonic-delta) approaches ε c ( r s ) = − π 2 / 360 ∼ − 0.02741 a.u., which agrees with the exact results in this limit [P.-F. Loos, ; V. Ashokan, , ]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance x = 0 to yield the same correlation energy. In contrast, other confinement potentials, V 3 ( q ) (infinite square well), V 4 ( q ) (infinite square-infinite triangular well), and V 6 ( q ) (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to ε c ∼ − 0.03002 a.u. for these potentials. The percentage difference in correlation energy between the confinement models V 1 ( q ) , V 2 ( q ) , V 5 ( q ) and V 3 ( q ) ,
We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths bbb and density parameters rs{r}_{\text{s}}rs​. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density. It is observed that the peak in the static structure factor at k=2kFk=2{k}_{\text{F}}k=2kF​ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter ${K}_{\ensuremath{\rho}}$ from the momentum density. It is found that ${K}_{\ensuremath{\rho}}$ increases by about 10% between wire widths b=0.01b=0.01b=0.01 and b=0.5b=0.5b=0.5. We also obtain ground-state properties of finite-thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b\ensuremath{\ll}{r}_{\text{s}}<1$. It is found that the correlation energy varies as b2{b}^{2}b2 for $b\ensuremath{\ll}{r}_{\text{s}}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of bbb and ${r}_{\text{s}}\ensuremath{\le}1$. These are compared with the QMC results in the range of applicability of the theory.
We calculate the ground-state energy of a quasi-one-dimensional electron gas with Coulomb interaction depending on the spin-polarization parameter and the Wigner-Seitz parameter . Cylindrical quantum wires of radius are considered. We describe the pair-correlation function g(z = 0) as a function of and . We derive the spin-susceptibility as a function of and in different approximations. Numerical results obtained for the spin-susceptibility are fitted by an analytical expression. Collective modes (charge-density and spin-density excitations) in cylindrical quantum wires are described and the validity range of our calculation is discussed.