We address the question of collective excitations in two-dimensional (2D) dipolar systems. The main issue is that such systems have no Hartree and no random-phase-approximation (RPA) limits and calculations have to include particle correlations from the outset. We focus on the longitudinal collective mode representing the density oscillations of the dipoles and on the transverse collective mode representing shear waves. Our theoretical approach is based on the quasi-localized charge approximation (QLCA) adapted to point-dipole systems interacting through a 1/ r 3 potential. Our analytical calculation is accompanied by classical molecular dynamics (MD) simulation. At long wavelengths, the longitudinal and transverse collective excitations exhibit acoustic behaviors with phase velocities that vary linearly with the dipole strength and are wholly maintained by particle correlations. At finite wavenumbers, the mode dispersion resulting from our classical MD simulations shows a roton-like behavior. Comparison with the quantum Monte Carlo dispersion generated through the Feynman relation (Astrakharchik et al 2007 Phys. Rev. Lett. 98 060405) shows a remarkably good quantitative agreement between the two.
We address the question of collective excitations in two-dimensional (2D) dipolar systems. The main issue is that such systems have no Hartree and no random-phase-approximation (RPA) limits and calculations have to include particle correlations from the outset. We focus on the longitudinal collective mode representing the density oscillations of the dipoles and on the transverse collective mode representing shear waves. Our theoretical approach is based on the quasi-localized charge approximation (QLCA) adapted to point-dipole systems interacting through a 1/ r 3 potential. Our analytical calculation is accompanied by classical molecular dynamics (MD) simulation. At long wavelengths, the longitudinal and transverse collective excitations exhibit acoustic behaviors with phase velocities that vary linearly with the dipole strength and are wholly maintained by particle correlations. At finite wavenumbers, the mode dispersion resulting from our classical MD simulations shows a roton-like behavior. Comparison with the quantum Monte Carlo dispersion generated through the Feynman relation (Astrakharchik et al 2007 Phys. Rev. Lett. 98 060405) shows a remarkably good quantitative agreement between the two.
The Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipolar systems has been studied recently by path integral Monte Carlo simulations [A. Filinov et al., Phys. Rev. Lett. 105, 070401 (2010)]. Here, we complement this analysis and study temperature-coupling strength dependence of the density (particle-hole) and single-particle (SP) excitation spectra both in superfluid and normal phases. The dynamic structure factor, $S(q,\ensuremath{\omega})$, of the longitudinal excitations is rigorously reconstructed with full information on damping. The SP spectral function, $A(q,\ensuremath{\omega})$, is worked out from the one-particle Matsubara Green's function. A stochastic optimization method is applied for reconstruction from imaginary times. In the superfluid regime sharp energy resonances are observed in both the density and SP excitations. The involved hybridization of both spectra is discussed. In contrast, in the normal phase, when there is no coupling, the density modes, beyond acoustic phonons, are significantly damped. Our results generalize previous zero-temperature analyses based on variational many-body wave functions [F. Mazzanti et al., Phys. Rev. Lett. 102, 110405 (2009); D. Hufnagl et al., Phys. Rev. Lett. 107, 065303 (2011)], where the underlying physics of the excitation spectrum and the role of the condensate has not been addressed.
We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long-wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero sound cannot propagate if the dipoles are perpendicular to the plane of confinement. At intermediate coupling, we find unstable modes that can lead either to collapse of the system or to the formation of a density wave. The BCS transition to a superfluid phase, on the other hand, occurs at arbitrarily weak strengths of the dipole-dipole interaction, provided the tilting angle exceeds a critical value. We determine the critical temperature of the transition, taking into account many-body effects as well as virtual transitions to higher excited states in the confining potential, and discuss prospects of experimental observations.
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation in a spherical geometry. It is shown that Laughlin's mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.
A two-component, two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, and the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure factor for the in-phase (symmetric) and out-of-phase (antisymmetric) collective modes during the dimerization is studied in detail with the stochastic reconstruction method and the method of moments. The antisymmetric mode spectrum is most strongly influenced by suppression of the inlayer superfluidity (specified by the superfluid fraction ${\ensuremath{\gamma}}_{s}={\ensuremath{\rho}}_{s}/\ensuremath{\rho}$). In a pure superfluid (normal fluid) phase, only an acoustic [optical (gapped)] mode is recovered. In a partially superfluid phase, both are present simultaneously, and the dispersion splits into two branches corresponding to a normal and a superfluid component. The spectral weight of the acoustic mode scales linearly with ${\ensuremath{\gamma}}_{s}$. This weight transfers to the optical branch when ${\ensuremath{\gamma}}_{s}$ is reduced due to formation of dimer states. In summary, we demonstrate how the interlayer dimerization in dipolar bilayers can be uniquely identified by static and dynamic properties.
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation In a spherical geometry. It is shown that Laughlin`s mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.
Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.