Self-consistent band-structure theory of the metal-insulator transition

The metal-insulator and magnetic transitions of a lattice of hydrogen atoms are investigated as a function of density at zero temperature. The density-functional method is used to produce self-consistent tight-binding band structures for possible paramagentic, ferromagnetic, and antiferromagnetic states. We find that the low-density antiferromagnetic crystal becomes a metal by band crossing near $r_s=2.5\mathrm{}$ (i.e., $n^{\frac{1}{3}}{a}_0=0.25\mathrm{}$) and a paramagnet near $r_s=2.2\mathrm{}$. The ferromagnetic state is never stable. Both transitions are continuous in our approximation. We compare our solution to this model to the Hubbard model and comment on the dielectric-catastrophe theory of Castner.