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

Physical Review Letters

Ground-State Properties of the Two-Dimensional Bose Coulomb Liquid

William R. Magro, David M. Ceperley

Published Aug 8, 1994• 46 citations
Publisher

Abstract

We present results of a ground-state study, via the diffusion Monte Carlo method, of a two-dimensional charged boson liquid. We observe three distinct behaviors in this system. At the lowest densities a close-packed Wigner crystal forms. At ${r}_{s}\ensuremath{\approx}12$ the crystal melts into a noncondensed liquid exhibiting algebraic off-diagonal long-range order; the single-particle density matrix decays as ${r}^{\ensuremath{-}\frac{{r}_{s}}{4}}$. Above a threshold density (${r}_{s}<8$), the long-wavelength momentum distribution diverges as ${k}^{\frac{({r}_{s}\ensuremath{-}8)}{4}}$, although no condensate forms.

DOI
10.1103/physrevlett.73.826

Related papers

Monte Carlo simulations of two-dimensional charged bosons

S. De Palo, Sergio Conti, Saverio Moroni

Quantum Monte Carlo methods are used to calculate various ground-state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at ${r}_{s}\ensuremath{\simeq}60.$ Results for the ground-state energy and the momentum distribution are summarized in analytic interpolation formulas embodying known asymptotic behaviors. Near freezing, the condensate fraction is less than 1%. The static structure factor $S(k)$ and susceptibility $\ensuremath{\chi}(k)$ are obtained from the density-density correlation function in imaginary time, $F(\mathbf{k},\ensuremath{\tau}).$ An estimate of the energy of elementary excitations, given in terms of an upper bound involving $S(k)$ and $\ensuremath{\chi}(k),$ is compared with the result obtained via analytic continuation from $F(\mathbf{k},\ensuremath{\tau}).$

arXiv:cond-mat/0306145•Physical Review B•Jan 22, 2004•32 citations

Bose-Einstein condensation in an interacting Bose liquid

Moshe Schwartz

An exact expression for the single-particle reduced density matrix of a translationally invariant system of bosons is obtained, as an average of a functional of the density and current operators. An approximation scheme, based on small fluctuations in density and current, is used in its lowest order, to approximate the single-particle reduced density matrix and the condensate density by a functional of the structure factor, which is a measurable quantity. This is done for the ground state and for finite temperatures. The resulting expressions for the condensate density are discussed. For the ideal gas the result is correct below the condensation temperature. For the case of an interacting liquid, Bose-Einstein condensation exists, in the ground states for two- and three-dimensional systems, and for finite temperatures it does exist only in three dimensions. The present experimental knowledge of the structure factor enables only a crude estimate of the condensed fraction which is found to be 0.1-0.2.

Physical Review A•Nov 1, 1974•11 citations

GROUND-STATE PROPERTIES OF A HOMOGENEOUS 2D SYSTEM OF BOSONS WITH DIPOLAR INTERACTIONS

G. E. ASTRAKHARCHIK, J. BORONAT, J. CASULLERAS +2 more

The ground-state phase properties of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo techniques. Limitations of mean-field theory in a two-dimensional geometry are discussed. A quantum phase transition from gas to solid is found. Crystal is tested for existence of a supersolid in the vicinity of the phase transition. Existence of mesoscopic analogue of the off-diagonal long-range order is shown in the one-body density matrix in a finite-size crystal. Non-zero superfluid fraction is found in a finite-size crystal, the signal being dramatically increased in presence of vacancies.

arXiv:0707.4630•Recent Progress in Many-Body Theories•Jun 1, 2008•1 citation

Exact ground-state properties of a one-dimensional Coulomb gas

G. E. Astrakharchik, Marvin D. Girardeau

The ground-state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground-state wave function which permits solution of the Fermi sign problem in the following respects: (i) the nodal surface is known, permitting exact calculations; and (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system and, thus, allowing simulation of a large number of fermions. Due to the mapping, the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground-state energy is calculated in homogeneous and trapped geometries using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the high-density ideal Fermi gas/Tonks-Girardeau limit, where low-lying excitations are phonons. Exact density profiles are compared to the ones calculated within the local density approximation, which predicts a change from a semicircular to an inverted parabolic shape of the density profile as the value of the charge is increased.

arXiv:1101.0103•Physical Review B•Apr 15, 2011•51 citations

Liquid State of One-Dimensional Bose Mixtures: A Quantum Monte Carlo Study

L. Parisi, G. E. Astrakharchik, S. Giorgini

By using exact quantum Monte Carlo methods we calculate the ground-state properties of the liquid phase in one-dimensional Bose mixtures with contact interactions. We find that the liquid state can be formed if the ratio of coupling strengths between interspecies attractive and intraspecies repulsive interactions exceeds a critical value. As a function of this ratio we determine the density where the energy per particle has a minimum and the one where the compressibility diverges, thereby identifying the equilibrium density and the spinodal point in the phase diagram of the homogeneous liquid. Furthermore, in the stable liquid state, we calculate the chemical potential, the speed of sound, as well as structural and coherence properties, such as the pair correlation function, the static structure factor, and the one-body density matrix, thus providing a detailed description of the bulk region in self-bound droplets.

arXiv:1810.07950•Physical Review Letters•Mar 14, 2019•104 citations

Ground state of a partially melted Wigner molecule

Zoltán Ádám Németh(a, Jean‐Louis Pichard

(received; accepted) PACS. 71.10-w – Theories and models for many-electron systems. PACS. 71.27+a – Strongly correlated electron systems. PACS. 73.20.Qt – Electron solids. Abstract. – We consider three spinless fermions free to move on 2d square lattice with periodic boundary conditions and interacting via a U/r Coulomb repulsion. When the Coulomb energy to kinetic energy ratio rs is large, a rigid Wigner molecule is formed. As rs decreases, we show that melting proceeds via an intermediate regime where a floppy two particle molecule coexists with a partially delocalized particle. A simple ansatz is given to describe the ground state of this mesoscopic solid-liquid regime. Ordered arrays of charged particles with long range Coulomb repulsion have been a continuous subject of interest in various branches of physics, including colloidal suspensions, ion rings, atomic-ion Wigner crystals, quantum computers, biophysics, plasmas, electrons deposited on liquid Helium surfaces, charges created in semiconductor or organic field effect devices. These

•Jan 1, 2002•2 citations
We present results of a ground-state study, via the diffusion Monte Carlo method, of a two-dimensional charged boson liquid. We observe three distinct behaviors in this system. At the lowest densities a close-packed Wigner crystal forms. At rs\ensuremath≈12{r}_{s}\ensuremath{\approx}12rs​\ensuremath≈12 the crystal melts into a noncondensed liquid exhibiting algebraic off-diagonal long-range order; the single-particle density matrix decays as r\ensuremath−rs4{r}^{\ensuremath{-}\frac{{r}_{s}}{4}}r\ensuremath−4rs​​. Above a threshold density (rs<8{r}_{s}<8rs​<8), the long-wavelength momentum distribution diverges as k(rs\ensuremath−8)4{k}^{\frac{({r}_{s}\ensuremath{-}8)}{4}}k4(rs​\ensuremath−8)​, although no condensate forms.
Quantum Monte Carlo methods are used to calculate various ground-state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at ${r}_{s}\ensuremath{\simeq}60.$ Results for the ground-state energy and the momentum distribution are summarized in analytic interpolation formulas embodying known asymptotic behaviors. Near freezing, the condensate fraction is less than 1%. The static structure factor S(k)S(k)S(k) and susceptibility $\ensuremath{\chi}(k)$ are obtained from the density-density correlation function in imaginary time, $F(\mathbf{k},\ensuremath{\tau}).$ An estimate of the energy of elementary excitations, given in terms of an upper bound involving S(k)S(k)S(k) and $\ensuremath{\chi}(k),$ is compared with the result obtained via analytic continuation from $F(\mathbf{k},\ensuremath{\tau}).$
An exact expression for the single-particle reduced density matrix of a translationally invariant system of bosons is obtained, as an average of a functional of the density and current operators. An approximation scheme, based on small fluctuations in density and current, is used in its lowest order, to approximate the single-particle reduced density matrix and the condensate density by a functional of the structure factor, which is a measurable quantity. This is done for the ground state and for finite temperatures. The resulting expressions for the condensate density are discussed. For the ideal gas the result is correct below the condensation temperature. For the case of an interacting liquid, Bose-Einstein condensation exists, in the ground states for two- and three-dimensional systems, and for finite temperatures it does exist only in three dimensions. The present experimental knowledge of the structure factor enables only a crude estimate of the condensed fraction which is found to be 0.1-0.2.
The ground-state phase properties of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo techniques. Limitations of mean-field theory in a two-dimensional geometry are discussed. A quantum phase transition from gas to solid is found. Crystal is tested for existence of a supersolid in the vicinity of the phase transition. Existence of mesoscopic analogue of the off-diagonal long-range order is shown in the one-body density matrix in a finite-size crystal. Non-zero superfluid fraction is found in a finite-size crystal, the signal being dramatically increased in presence of vacancies.
The ground-state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground-state wave function which permits solution of the Fermi sign problem in the following respects: (i) the nodal surface is known, permitting exact calculations; and (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system and, thus, allowing simulation of a large number of fermions. Due to the mapping, the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground-state energy is calculated in homogeneous and trapped geometries using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the high-density ideal Fermi gas/Tonks-Girardeau limit, where low-lying excitations are phonons. Exact density profiles are compared to the ones calculated within the local density approximation, which predicts a change from a semicircular to an inverted parabolic shape of the density profile as the value of the charge is increased.
By using exact quantum Monte Carlo methods we calculate the ground-state properties of the liquid phase in one-dimensional Bose mixtures with contact interactions. We find that the liquid state can be formed if the ratio of coupling strengths between interspecies attractive and intraspecies repulsive interactions exceeds a critical value. As a function of this ratio we determine the density where the energy per particle has a minimum and the one where the compressibility diverges, thereby identifying the equilibrium density and the spinodal point in the phase diagram of the homogeneous liquid. Furthermore, in the stable liquid state, we calculate the chemical potential, the speed of sound, as well as structural and coherence properties, such as the pair correlation function, the static structure factor, and the one-body density matrix, thus providing a detailed description of the bulk region in self-bound droplets.
(received; accepted) PACS. 71.10-w – Theories and models for many-electron systems. PACS. 71.27+a – Strongly correlated electron systems. PACS. 73.20.Qt – Electron solids. Abstract. – We consider three spinless fermions free to move on 2d square lattice with periodic boundary conditions and interacting via a U/r Coulomb repulsion. When the Coulomb energy to kinetic energy ratio rs is large, a rigid Wigner molecule is formed. As rs decreases, we show that melting proceeds via an intermediate regime where a floppy two particle molecule coexists with a partially delocalized particle. A simple ansatz is given to describe the ground state of this mesoscopic solid-liquid regime. Ordered arrays of charged particles with long range Coulomb repulsion have been a continuous subject of interest in various branches of physics, including colloidal suspensions, ion rings, atomic-ion Wigner crystals, quantum computers, biophysics, plasmas, electrons deposited on liquid Helium surfaces, charges created in semiconductor or organic field effect devices. These