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=-2{^2n}mlnn{a^2} and n₀=n (1+1lnn{a^2}), where n is the areal density of the system. The expansion parameter -1lnn{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.