We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multimode optical cavities. The solution of an infinite-range model yields a metallic phase, which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional disordered Fermi liquid, and the insulating electron glass of semiconductors. Prospects for the realization of such glassy phases in cold-atom systems are discussed.
We present a first principles description of the interaction of two ground-state scandium atoms. Scandium has a
2Dg ground state. Thirty molecular states correlate to the lowest dissociation limit of the dimer. In the short range, potential energy curves are calculated using second-order
n-electron valence state perturbation theory. The first-order long-range interaction is calculated at the complete active space self-consistent field level. We determine the second-order long-range dispersion interaction from atomic dynamic polarizabilities at imaginary frequencies. These polarizabilities are calculated using time-dependent density functional theory. We merge the short-range approach with the long-range model to obtain a physical description of the 30 potential energy curves correlating to the
2Dg+2Dg limit. Diabatic potentials are presented that can be used in quantum scattering calculations, in order to study Zeeman relaxation of ultracold scandium atoms.