Two-Dimensional System of Hard-Core Bosons

Abstract

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 $\frac{E}{N}=\ensuremath{-}\frac{2\ensuremath{\pi}{\ensuremath{\hbar}}^{2}n}{m\mathrm{ln}n{a}^{2}}$ and ${n}_{0}=n(1+\frac{1}{\mathrm{ln}n{a}^{2}})$, where $n$ is the areal density of the system. The expansion parameter $\ensuremath{-}\frac{1}{\mathrm{ln}n{a}^{2}}$ 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.