Variational density matrix approach to the temperature-dependent elementary excitation spectrum of two-dimensional liquid4He

Using the variational density matrix method, we obtain a temperature-dependent elementary excitation spectrum for two-dimensional liquid⁴He. For more precise results, we use a Jastrow-Feenberg-type trial wave function and include the contribution of elementary diagrams within the hypernetted chain approximation. The behavior of the excitation spectrum as a function of the temperature and density in two dimensions is similar to that of the bulk system, but has a smaller roton minimum. The roton minimum of the excitation spectrum decreases with increasing temperature and increases with increasing density at low densities but decreases at large densities. The results agree well with Monte Carlo calculations and are closer than pevious theories to experimental measurements of⁴He film adsorbed on substrates.