Split Hubbard bands at low densities

Abstract

We present a numerical scheme for the Hubbard model that throws light on the rather esoteric nature of the upper and lower Hubbard bands, which have been invoked often in literature. We present a self-consistent solution of the ladder-diagram equations for the Hubbard model, and show that these provide, at least in the limit of low densities of particles, a vivid picture of the Hubbard split bands. We also address the currently topical problem of decay of the doublon states that are measured in optical trap studies, using both the ladder scheme and also an exact two-particle calculation of a relevant Green's function.