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:2605.26420 · Physical review. B./Physical review. B

Ground-state correlations in the one-dimensional Fermi one-component plasma

Anonymous

Published Jul 17, 2026• 0 citations
arXivHTMLPDF

Abstract

Structural and dynamic correlations in the ground state of the one-dimensional Fermi one-component plasma are studied by Quantum Monte Carlo simulations. Results are presented for the pair correlation function, static structure factor, the one-particle density matrix and the momentum distribution, for the cases of full, partial and no polarization. {Within the precision of the calculation, the results conform to the fundamental scaling prediction of the Tomonaga-Luttinger Liquid Theory}. Evidence is reported of density correlations slowly decaying with distance, with the concurrent emergence of quasi-crystalline order even in the weakly correlated regime. Effects of quantum statistics in the momentum distribution are discussed.

DOI
10.1103/g3hl-w584

Related papers

Luttinger-liquid behavior of one-dimensional He3

G. E. Astrakharchik, Jordi Boronat

The ground-state properties of one-dimensional $^{3}\mathrm{He}$ are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a ``Bose gas.'' a ``super-Tonks-Girardeau'' regime, and a ``quasicrystal.'' The obtained results are applicable to unpolarized, partially, or fully polarized $^{3}\mathrm{He}$.

arXiv:1408.1565•Physical Review B•Dec 30, 2014•26 citations

Correlation functions and momentum distribution of one-dimensional Bose systems

G. E. Astrakharchik, S. Giorgini

The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix, and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.

arXiv:cond-mat/0212512•Physical Review A•Sep 5, 2003•106 citations

One-dimensional electron fluid at high density

Vinod Ashokan, N. D. Drummond, K. N. Pathak

We calculate the ground-state energy, pair correlation function, static structure factor, and momentum density of the one-dimensional electron fluid at high density using variational quantum Monte Carlo simulation. For an infinitely thin cylindrical wire the predicted correlation energy is found to fit nicely with a quadratic function of coupling parameter ${r}_{s}$. The extracted exponent $\ensuremath{\alpha}$ of the momentum density for $k\ensuremath{\sim}{k}_{F}$ is used to determine the Tomonaga-Luttinger parameter ${K}_{\ensuremath{\rho}}$ as a function of ${r}_{s}$ in the high-density regime. We find that the simulated static structure factor and pair correlation function for infinitely thin wires agree with our recent high-density theory [K. Morawetz et al., Phys. Rev. B 97, 155147 (2018)].

arXiv:1805.00344•Physical review. B./Physical review. B•Sep 24, 2018•12 citations

Ground-state properties of the one-dimensional electron liquid

R. M. Lee, N. D. Drummond

We present calculations of the energy, pair-correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around ${k}_{\mathrm{F}}$, finding good agreement between the exponent of the ferromagnetic infinitely thin wire and the ferromagnetic harmonic wire.

arXiv:1102.3854•Physical Review B•Jun 22, 2011•47 citations

Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid

N. D. Drummond, Richard J. Needs

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

arXiv:1002.2122•Physical Review B•Feb 13, 2009•40 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
Structural and dynamic correlations in the ground state of the one-dimensional Fermi one-component plasma are studied by Quantum Monte Carlo simulations. Results are presented for the pair correlation function, static structure factor, the one-particle density matrix and the momentum distribution, for the cases of full, partial and no polarization. {Within the precision of the calculation, the results conform to the fundamental scaling prediction of the Tomonaga-Luttinger Liquid Theory}. Evidence is reported of density correlations slowly decaying with distance, with the concurrent emergence of quasi-crystalline order even in the weakly correlated regime. Effects of quantum statistics in the momentum distribution are discussed.
The ground-state properties of one-dimensional 3He^{3}\mathrm{He}3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a ``Bose gas.'' a ``super-Tonks-Girardeau'' regime, and a ``quasicrystal.'' The obtained results are applicable to unpolarized, partially, or fully polarized 3He^{3}\mathrm{He}3He.
The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix, and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.
We calculate the ground-state energy, pair correlation function, static structure factor, and momentum density of the one-dimensional electron fluid at high density using variational quantum Monte Carlo simulation. For an infinitely thin cylindrical wire the predicted correlation energy is found to fit nicely with a quadratic function of coupling parameter rs{r}_{s}rs​. The extracted exponent $\ensuremath{\alpha}$ of the momentum density for $k\ensuremath{\sim}{k}_{F}$ is used to determine the Tomonaga-Luttinger parameter ${K}_{\ensuremath{\rho}}$ as a function of rs{r}_{s}rs​ in the high-density regime. We find that the simulated static structure factor and pair correlation function for infinitely thin wires agree with our recent high-density theory [K. Morawetz et al., Phys. Rev. B 97, 155147 (2018)].
We present calculations of the energy, pair-correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around kF{k}_{\mathrm{F}}kF​, finding good agreement between the exponent of the ferromagnetic infinitely thin wire and the ferromagnetic harmonic wire.
We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.
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.