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:cond-mat/0612691 · Physical Review A

Weakly interacting two-dimensional system of dipoles: Limitations of the mean-field theory

G. E. Astrakharchik, Jordi Boronat, J. Casulleras, I. L. Kurbakov, Yu. E. Lozovik

Published Jun 29, 2007• 25 citations
arXivHTMLPDF

Abstract

We consider a homogeneous two-dimensional Bose gas with repulsive dipole-dipole interactions. The ground-state equation of state, calculated using the diffusion Monte Carlo method, shows quantitative differences from the predictions of the commonly used Gross-Pitaevskii mean-field theory. The static structure factor, pair distribution function, and condensate fraction are calculated in a wide range of the gas parameter. Differences from mean-field theory are reflected in the frequency of the lowest ``breathing'' mode for harmonically trapped systems.

DOI
10.1103/physreva.75.063630

Related papers

Ground state of a homogeneous Bose gas: A diffusion Monte Carlo calculation

S. Giorgini, Jordi Boronat, J. Casulleras

We use a diffusion Monte Carlo method to calculate the lowest-energy state of a uniform gas of bosons interacting through different model potentials, both strictly repulsive and with an attractive well. We explicitly verify that at low density the energy per particle follows a universal behavior fixed by the gas parameter ${\mathrm{na}}^{3}.$ In the regime of densities typical for experiments in trapped Bose-condensed gases, the corrections to the mean-field energy greatly exceed the differences due to the details of the potential.

arXiv:cond-mat/9902185•Physical Review A•Dec 1, 1999•149 citations

Microscopic description of anisotropic low-density dipolar Bose gases in two dimensions

A. Macia, Ferran Mazzanti, Jordi Boronat +1 more

A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.

arXiv:1105.5914•Physical Review A•Sep 19, 2011•36 citations

Quantum Monte Carlo simulation of a two-dimensional Bose gas

Sebastiano Pilati, Jordi Boronat, J. Casulleras +1 more

The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite ranged and strictly repulsive and zero ranged, supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gaslike state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.

arXiv:cond-mat/0411049•Physical Review A•Feb 11, 2005•51 citations

Two-dimensional weakly interacting Bose gas: equation of state

G. E. Astrakharchik, Jordi Boronat, J. Casulleras +2 more

The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as na^2 ~ 10^{-100} permits us for the first time to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e. entirely described by the gas parameter na^2). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.

arXiv:0812.3844•Dec 19, 2008•0 citations

Equation of state of a weakly interacting two-dimensional Bose gas studied at zero temperature by means of quantum Monte Carlo methods

G. E. Astrakharchik, Jordi Boronat, J. Casulleras +2 more

The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as $n{a}^{2}\ensuremath{\propto}{10}^{\ensuremath{-}100}$ permits us to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e., entirely described by the gas parameter $n{a}^{2}$). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.

Physical Review A•May 12, 2009•42 citations

Many-body dimensional perturbation theory for quantum confined systems with a focus on atomic gas Bose-Einstein condensates

Brett Allen McKinney

Feshbach resonances notwithstanding, most experimentally realized atomic-vapor condensates are dilute and are best described by the mean-field Gross-Pitaevskii equation. For this reason, we use dimensional scaling methods to obtain an analytical approximation to the GP equation that is more accurate and flexible than the commonly used ground-state Thomas-Fermi approximation. We also demonstrate the power of dimensional perturbation theory by providing a full solution of a model BEC Hamiltonian and a two-electron quantum dot Hamiltonian. A feature shared by these examples is the high degree of accuracy provided by the lowest orders of the perturbation theory. In our approach to the full many-body BEC Hamiltonian, we use the lowest orders of many-body dimensional perturbation theory to obtain semi-analytical ground-state energies and collective excitation frequencies. Our many-body calculations for BEC's compare well with the Gross-Pitaevskii results in the weakly-interacting regime, as they should, and are much improved over mean-field theory predictions in the strongly-interacting regime.

•Jan 1, 2003•0 citations
We consider a homogeneous two-dimensional Bose gas with repulsive dipole-dipole interactions. The ground-state equation of state, calculated using the diffusion Monte Carlo method, shows quantitative differences from the predictions of the commonly used Gross-Pitaevskii mean-field theory. The static structure factor, pair distribution function, and condensate fraction are calculated in a wide range of the gas parameter. Differences from mean-field theory are reflected in the frequency of the lowest ``breathing'' mode for harmonically trapped systems.
We use a diffusion Monte Carlo method to calculate the lowest-energy state of a uniform gas of bosons interacting through different model potentials, both strictly repulsive and with an attractive well. We explicitly verify that at low density the energy per particle follows a universal behavior fixed by the gas parameter na3.{\mathrm{na}}^{3}.na3. In the regime of densities typical for experiments in trapped Bose-condensed gases, the corrections to the mean-field energy greatly exceed the differences due to the details of the potential.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite ranged and strictly repulsive and zero ranged, supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gaslike state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.
The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as na^2 ~ 10^{-100} permits us for the first time to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e. entirely described by the gas parameter na^2). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.
The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as $n{a}^{2}\ensuremath{\propto}{10}^{\ensuremath{-}100}$ permits us to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e., entirely described by the gas parameter na2n{a}^{2}na2). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.
Feshbach resonances notwithstanding, most experimentally realized atomic-vapor condensates are dilute and are best described by the mean-field Gross-Pitaevskii equation. For this reason, we use dimensional scaling methods to obtain an analytical approximation to the GP equation that is more accurate and flexible than the commonly used ground-state Thomas-Fermi approximation. We also demonstrate the power of dimensional perturbation theory by providing a full solution of a model BEC Hamiltonian and a two-electron quantum dot Hamiltonian. A feature shared by these examples is the high degree of accuracy provided by the lowest orders of the perturbation theory. In our approach to the full many-body BEC Hamiltonian, we use the lowest orders of many-body dimensional perturbation theory to obtain semi-analytical ground-state energies and collective excitation frequencies. Our many-body calculations for BEC's compare well with the Gross-Pitaevskii results in the weakly-interacting regime, as they should, and are much improved over mean-field theory predictions in the strongly-interacting regime.