Origin of the Mott gap

We show exactly that the only charged excitations that exist in the strong-coupling limit of the half-filled Hubbard model are gapped composite excitations generated by the dynamics of the charge 2e boson that appears upon explicit integration of the high-energy scale. At every momentum, such excitations have nonzero spectral weight at two distinct energy scales separated by the on-site repulsion U. The result is a gap in the spectrum for the composite excitations accompanied by a discontinuous vanishing of the density of states at the chemical potential when U exceeds the bandwidth. Consequently, we resolve the long-standing problem of the cause of the charge gap in a half-filled band in the absence of symmetry breaking.