Nature of Split Hubbard Bands at Low Densities

TL;DR

This paper introduces a numerical scheme for the Hubbard model that clarifies the nature of Hubbard bands at low densities and investigates doublon decay using ladder diagrams and exact two-particle calculations.

Contribution

It provides a self-consistent ladder diagram solution revealing the properties of Hubbard bands at low densities and analyzes doublon decay mechanisms.

Findings

Ladder diagram equations elucidate Hubbard band structure at low densities.

The scheme offers a vivid picture of Hubbard split bands.

Doublon decay is characterized through both ladder scheme and exact two-particle calculations.

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 that 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 the ladder scheme and also by an exact two particle calculation of a relevant Greens function.