Absorption in a strong-coupling half-filled-band Hubbard chain

A theory of absorption is presented for a half-filled Hubbard band with nearest-neighbour electron transfer (t) and strong intra-site Coulomb repulsion (U). The lineshape is calculated at low temperature (i.e. k B T<<U) to lowest order in t/U for antiferromagnetic, random and ferromagnetic spin configurations in a Cayley tree lattice with a particular emphasis on one dimension. The authors find that the absorption diverges logarithmically at the centre of the absorption band (i.e. at h(cross) omega =U). In a one-dimensional lattice, the absorption width equals twice the bandwidth of a single hole (or an extra electron) in an otherwise half-filled Hubbard band.