The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from gas to solid phase when the density increases. In the gas phase the condensate fraction is calculated as a function of the density. Using Feynman approximation, the collective excitation branch is studied and appearance of a roton minimum is observed. Results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindeman ratio at the transition point comes to be γ = 0.230(6). The condensate fraction in the gas phase is estimated as a function of the density.The chromium atom has exceptionally large permanent dipole moment and recent realization of Bose-Einstein condensation of 52 Cr[1] has stimulated great interest in properties of dipolar systems at low temperatures. It was observed[2] that dipolar forces lead to anisotropic deformation during expansion of the condensate. In the experiments [1,2], the dipolar forces were competing with short-range scattering. The latter, in principle, can be removed by tuning the s-wave scattering length to zero by Feshbach resonance [3]. This would lead to an essentially pure system of dipoles. On the other hand, lowdimensional systems can be realized by making the confinement in one (or two) directions so tight, that no excitations of the levels of the tight confinement are possible and the system is dynamically two-(or one-) dimensional.A major development has also been done in the present years towards the realization of excitons at temperatures close to the Bose-Einstein condensation temperature [4]. An exciton is much more stable if the electron is spatially separated from the hole (spatially separated excitons). Such an exciton can be modeled as a dipole. If the excitons are in two coupled quantum wells they can be treated effectively as two-dimensional if the size of an exciton is small compared to the mean distance between excitons.One might expect to find a phase transition from gas phase to a crystal one at large density. As the condensate fraction is small at the transition point, perturbative theories, like Gross-Pitaevskii [5] or Bogoliubov [6,7] approaches, will fail to describe accurately this transition. One has to use ab initio numerical methods to address this quantum many-body problem. Recently a trapped system of two-dimensional dipoles has been studied by Path Integral Monte Carlo method [8] and mesoscopic analog of crystallization has been found. Trapped dipoles with s-wave scattering were investigated [9]. So far, there have been no full quantum microscopic computations of the properties of a homogeneous system of dipoles.The Hamiltonian of a homogeneous system of N bosonic dipoles has the formwhere M is the dipole mass and r i , i = 1, N are the positions of dipoles. The expression for the coupling constant C dd depends on the nature of the dipole-dipole interaction. Two possible physical realizations of a twodim...

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.

By doing quantum Monte Carlo ab initio simulations we show that dipolar excitons, which are now under experimental study, actually are strongly correlated systems. Strong correlations manifest in significant deviations of excitation spectra from the Bogoliubov one, large Bose condensate depletion, short-range order in the pair correlation function, and peak(s) in the structure factor.PACS numbers: 71.35. Lk, 03.75.Hh, 02.70.Ss, 73.21.Fg Two-dimensional (2D) dipolar excitons (DEs) with spatially separated electrons (e) and holes (h) are extremely interesting due to increased lifetime, which permits to achieve different quasi-equilibrium exciton phases predicted for the system, e.g., 2D DE superfluid in extended systems [1, 2,3,4,5] [14,15,16,17,18,19] and SQW [20].The superfluidity and coherent properties of equilibrium e-h systems (in a sense of "spatially separated semimetal") have been also theoretically studied [1, 2,4,11]. An important progress was achieved by studying an electron bilayer in high magnetic field with 1/2 + 1/2 filling of Landau levels [21]. It can be proved that the properties of the system can be presented as a BCS state of a spatially separated (composite fermion) e-h system at zero magnetic field [1, 2,22]. The predicted e-h superfluidity and Josephson-like effects in this system were observed later on experimentally [23]. It is worth noticing that the 2D dipolar Bose systems under consideration have been recently realized in atomic systems with large dipolar moments (e.g., for Cr atoms) [24] and polar molecules [25].The majority of theoretical models describe the excitonic Bose condensate as an ideal or weakly correlated gas. Unfortunately, these approaches have a very limited region of applicability. Indeed, at small densities the repulsive dipole-dipole potential can be described by one parameter a, the s-wave scattering length, and the properties are expected to be universal, i.e., to be the same for all interaction potentials having the same value of scattering length and, in particular, to be the same as in a system of hard-disks of diameter a. In fact, the latter is known to be weakly correlated only in ultra-rarified systems [7]. So, the model of weakly correlated excitons holds only in ultra-rarified gases which have extremely low critical temperature. For real experimental excitonic densities such models can provide only a qualitative description. Thus, a more accurate model should be worked out and a more precise study should be done in order to describe 2D DEs in quantum wells (QWs).This paper is devoted to a detailed microscopic study of 2D DEs by means of the diffusion Monte Carlo (DMC) technique. We prove that excitons are in fact strongly correlated in all the main up-to-now experiments with CQW [16,17,18] in which low-temperature collective effects in exciton luminescence have been observed. We have obtained the following results supporting this fact:(i) The dimensionless compressibility ζ = (m 3 /2π 2 )/χ and the contribution of dipole-dipole collisions to the chemical...

We consider a homogeneous 2D Bose gas with repulsive dipole-dipole interactions. The groundstate equation of state, calculated using the Diffusion Monte Carlo method, shows quantitative differences with predictions of 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 with mean-field theory are reflected in the frequency of the lowest "breathing" mode for harmonically trapped systems. PACS numbers: 51.30.+i, 03.75.Hh, 71.27.+a The study of quasi-two-dimensional Bose gases at ultra-low temperatures has become a very active area of research. The role of correlations and quantum fluctuations is greatly enhanced in reduced dimensionality making a two-dimensional (2D) system well suited for studying beyond mean-field effects. The superfluidnormal phase transition occurs at a finite-temperature and follows the peculiar scenario of Berezinskii, Kosterlitz, Thouless [1]. On the contrary, the system undergoes Bose-Einstein condensation (BEC) only at zero temperature[2], since long-wavelength phase fluctuations destroy long-range order. The analytical descriptions of 2D systems include mean-field Gross-Pitaevskii (GPE) theory [3,4], beyond mean-field approaches [5,6], and numerical methods [7,8,9].

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent s-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.