Order in dense hydrogen at low temperatures

By increase in density, impelled by pressure, the electronic energy bands in dense hydrogen attain significant widths. Nevertheless, arguments can be advanced suggesting that a physically consistent description of the general consequences of this electronic structure can still be constructed from interacting but state-dependent multipoles. These reflect, in fact self-consistently, a disorder-induced localization of electron states partially manifesting the effects of proton dynamics; they retain very considerable spatial inhomogeneity (as they certainly do in the molecular limit). This description, which is valid provided that an overall energy gap has not closed, leads at a mean-field level to the expected quadrupolar coupling, but also for certain structures to the eventual emergence of dipolar terms and their coupling when a state of broken charge symmetry is developed. A simple Hamiltonian incorporating these basic features then leads to a high-density, low-temperature phase diagram that appears to be in substantial agreement with experiment. In particular, it accounts for the fact that whereas the phase I-II phase boundary has a significant isotope dependence, the phase II-III boundary has very little.