We consider the charge excitations of the half-filled Hubbard chain, which are related to electron pairs occupying the same lattice site. In the exact Bethe Ansatzeigen function, we separate the centre-off-mass motion by introducing the centre off-mass and relative coordinates and wave vectors. These excitations are then interpreted as interacting quasi-particles propagating as plane waves along the chain. The two-body problem is solved for these quasi-particles. The solution suggests the existence of bound pairs, namely particle-hole excitonic states. A connection to the magnon states of the ferromagnetic Heisenberg chain is also discussed.
Whatever was going to replace classical physics in the description of radiation and atomic phenomena had to confront the difficult task of somehow reconciling the wave-like and particle-like aspects of light in a single structure. An important clue would come from Einstein’s E=mc2. We tend to want to associate mass (and linear momentum) with material particles. But the Planck–Einstein relation E=hν connects energy with frequency, a determinedly wave-like property. So, here are two very simple yet fundamental equations connecting energy to mass and energy to frequency. Can they be combined? Louis de Broglie thought so, and in 1923 he generalized the discovery made by Einstein in 1905 by extending it to all material particles, and most notably to electrons. The de Broglie relation λ=h/p can be derived quite straightforwardly by comparing the Lorentz transformations for energy and momentum with those for a system of plane waves.