VARIATIONAL DENSITY-MATRIX APPROACH TO THE TEMPERATURE-DEPENDENT ELEMENTARY EXCITATION SPECTRUM OF 2-DIMENSIONAL LIQUID-HE-4

Using the variational density matrix method, we obtain a temperature-d ependent elementary excitation spectrum for two-dimensional liquid He- 4. Ebv more precise results, we use a Jastrow-Feenberg-type trial wave function aad include the contribution of elementary diagrams within t he hypernetted chain approximation. The behavior of the excitation spe ctrum as a function of the temperature and density in two dimensions i s similar to that of the bulk system, but has a smaller roton minimum. The roton minimum of the excitation spectrum decreases with increasin g temperature and increases with increasing density at low densities b ut decreases at large densities. The results agree well with Monte Car lo calculations and ave closer than pevious theories to experimental m easurements of He-4 film adsorbed on substrates.