Microscopic theory of two-dimensional liquid helium

Starting with real boson particles interacting with a soft potential, it is shown that the excitation spectrum and thermodynamical properties of the system in two dimensions are characterized by the Landau-type quasiparticles. The structure factor, specific heat, and the pair distribution function are explicitly evaluated. The pair-distribution function decreases as $r^{-3\mathrm{}}$ at large distances. This decrease corresponds to the existence of a phonon spectrum for small momenta. The normal-fluid density divided by the product of the mass density and absolute temperature cubed is constant near absolute zero, reaches to a minimum, and increases at around 0.4 °K. The roton energy gap is given by the position of the minimum energy and the structure factor at this point. Our value is what we might expect by extrapolating the data by Washburn, Rutledge, and Mochel. It also agrees with the recent result by Rutledge, McMillan, and Mochel. The ground-state energy is also evaluated analytically.