Origin of the Mott Gap

TL;DR

This paper demonstrates that in the strong-coupling limit of the half-filled Hubbard model, the charge gap arises from gapped composite excitations involving a charge 2e boson, explaining the origin of the Mott gap without symmetry breaking.

Contribution

It provides an exact analysis showing the charge gap originates from composite excitations generated by a charge 2e boson in the strong-coupling Hubbard model.

Findings

Charge excitations are gapped composite states.

Spectral weight appears at two energy scales separated by U.

The charge gap appears without symmetry breaking.

Abstract

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 non-zero 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.