The electronic structure of a liquid of interacting hydrogenic atoms: A prototype for expanded liquid metals

The electronic structure of a metal heated above its critical temperature (an ``expanded liquid metal'') shows dramatic changes as the density is increased. There is some experimental evidence that as one proceeds from insulating to metallic behavior the substance can even go through two separate phase transitions: from an ordinary insulator to a so-called excitonic insulator, and then from an excitonic insulator to a metal. In an effort to study how the metallic phase is approached, we have used discretized-path-integral methods to look at the statistical mechanics and the electronic structure of a model liquid. In the gas phase, the atoms in the model have a single valence electron constrained to occupy one of the s or p orbitals of the valence shell, but at higher densities, the orbitals hybridize, leading to instantaneous dipole-dipole interaction. We show that formulating this electronic structure in terms of occupation numbers allows us to monitor the hybridization evolution via an imaginary-time correlation function—which we calculate from an analytical solution to the mean-spherical approximation for the model. The numerical results strongly suggest that the model has a sudden hybridization transition, suggesting, in turn, that it might be profitable to think of the excitonic insulator transition in this language.