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

Abstract

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.

Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

“…A series of our previous works has been devoted to the study of the equation of state of dilute 2D Bose gases [24,[42][43][44][45][46][47]. A number of interaction potentials (dipolar, hard disks, etc.)…”

“…Historically, it turned out to be very difficult to obtain the correct expression for this term, see Ref. [24] for a summary of different results. Only recently has the correct expression been obtained [21][22][23]52].…”

“…Only recently has an analytical expression for the equation of state of a two-dimensional (2D) Bose gas in the low density regime na 2 < ∼ 10 −3 been correctly derived [21][22][23] and checked numerically [24]. In these works the interaction potential is described only by the s-wave scattering length a.…”

Strongly Interacting Two-Dimensional Bose Gases

“…Interacting Bose gases in two dimensions and BKT physics have been actively investigated in many condensed matter experiments [3][4][5][6][7]. In cold atoms, the BKT transition and the suppression of fluctuations are observed based on 2D gases in the weak interaction regimes [8][9][10][11].Extensive theoretical research on 2D Bose systems addresses the role of interactions in the superfluid phase [12][13][14][15][16][17] and near the BKT critical point [18,19]. In the weak interaction regime, the classical φ 4 field theory [18,19] predicts the logarithmic corrections to the critical chemical potential µ c = k B T (g/π) ln(13.2/g) and the critical density n c = λ −2 dB ln(380/g) for small two-body interaction strength g < 0.2.…”

“…Here, m is the mass of the boson, n is the density, and 2π is the Planck constant. Defining the superfluid coupling constant as G = m/( 2 κ), where κ = ∂n/∂µ is the compressibility, we can summarize the perturbation expansion result of G as [12] …”