Quantum Monte Carlo simulation of a two-dimensional Bose gas

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.

Figure 1

Energy per particle as a function of the gas parameter for the HD potential. Solid line: mean-field result, Eq. (1). Error bars are smaller than the size of the symbols.

Figure 2

Beyond mean-field corrections to the equation of state. Circles, HD potential; triangles, SD potential; squares, PP potential. Dashed line: numerical fit to the results of the HD potential, Eq. (16). Error bars are smaller than the size of the symbols. Inset: region of extremely dilute systems $n{a}_{2D}^2⩽{10}^{-6}$.

Figure 3

Energy per particle and inverse compressibility as a function of the gas parameter. Symbols are as in Fig. 2. Thick and thin dashed lines: best fit (16) to the HD equation of state and corresponding $m{c}^2$, respectively. Thick and thin solid lines: polynomial best fit to the PP equation of state and corresponding $m{c}^2$, respectively. Error bars are smaller than the size of the symbols.

Figure 4

Condensate fraction as a function of the gas parameter. Circles, HD potential; triangles, SD potential. Solid line: result from Bogoliubov theory, Eq. (17).

Figure 5

Pair distribution function of a HD gas obtained for three values of the gas parameter: $n{a}_{2D}^2={10}^{-4}$, solid line; $n{a}_{2D}^2=0.01$, dashed line; $n{a}_{2D}^2=0.1$, dotted line.