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 EN=-2πℏ²nmlnna² and n₀=n(1+1lnna²), where n is the areal density of the system. The expansion parameter -1lnna² 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.