Two-Dimensional System of Hard-Core Bosons

As a model of a helium monolayer a system of hard-core bosons of mass $m$ and diameter $a$ constrained to motion in two dimensions is considered at absolute zero. In the low-density limit, the ground-state energy per particle and condensate depletion are found to be $\frac{E}{N}=-\frac{2\pi {\hslash }^{2}n}{m\ln n{a}^2}$ and $n_0=n(1+\frac{1}{\ln n{a}^2})$, where $n$ is the areal density of the system. The expansion parameter $-\frac{1}{\ln n{a}^2}$ is approximately equal to unity for real helium monolayers. The variation of the above results with temperature is discussed for a system of finite size.