Excitations with complex wavenumbers in a Hubbard chain. I. States with one pair of complex wavenumbers

Abstract

Those excited states of a half-filled 1D Hubbard chain that are connected with electron pairs occupying the same site are studied. It is argued that these states should be described by solutions of the Lieb-Wu equations (1968) in which some of the wavenumbers are complex. Solutions of this type have been found that correspond to states in which the spin part is not excited. The energy-momentum dispersion is also calculated. The gap in the spectrum of the single excitations equals the discontinuity of the chemical potential calculated by Lieb and Wu.