Gutzwiller-Hubbard lattice-gas model with variable density: Application to normal liquidHe3

The results of the Gutzwiller approach to a Hubbard lattice-gas model with a variable density of particles is used to describe the pressure dependence of thermodynamic properties of the ground state of normal liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The molar volume of the liquid is given by that of the underlying lattice and the filling factor n=1-δ of the band, where δ describes the deviation from half-filling. If the lattice is taken as incompressible, one finds that there exists a critical pressure at which a transition to a localized state occurs. The transition is accompanied by a disappearance of δ, i.e., the transition only takes place at exactly half-filling. As the transition is approached, δ and the density of doubly occupied sites are found to scale. The pressure dependence of the effective mass, the spin susceptibility and the compressibility is calculated. In a second model, the lattice is assumed to be compressible, shifting the critical pressure to much higher values. The on-site repulsion U is related to the microscopic soft-core potential $f_0^s$(r), which allows one to calculate the pressure dependence of the effective mass and the spin susceptibility. The absence of a localization transition for pressures of the order of the melting pressure of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ leads to a smooth pressure dependence of the calculated quantities which are qualitatively borne out by experiment.