Physical picture of the gapped excitation spectrum of the one-dimensional Hubbard model Original Research Article

A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-ansatz approach. This approach allows us to prove a “string hypothesis” for complex momenta and derive an exact formulation of the Bethe-ansatz equations including all states. Among other things we show that all gapped eigenstates have the Bethe-ansatz form, contrary to assertions in the literature [Essler et al., Nucl. Phys. B 372 (1992) 559]. The simplest excitations in the upper Hubbard band are computed: we find an unusual dispersion close to half-filling.