  We study the Coulomb glass emerging from the interplay of strong interactions
and disorder in a model of spinless fermions on the Bethe lattice. In the
infinite coordination number limit, strong interactions induce a metallic
Coulomb glass phase with a pseudogap structure at the Fermi energy. Quantum and
thermal fluctuations both melt this glass and induce a disordered quantum
liquid phase. We combine self-consistent diagrammatic perturbation theory with
continuous time quantum Monte-Carlo simulations to obtain the complete phase
diagram of the electron glass, and to characterize its dynamical properties in
the quantum liquid, as well as in the replica symmetry broken glassy phase.
Tunneling spectra display an Efros-Shklovskii pseudogap upon decreasing
temperatures, but the density of states remains finite at the Fermi energy due
to residual quantum fluctuations. Our results bear relevance to the metallic
glass phase observed in Si inversion layers.
