Fractional and Integer Excitations in Quantum Antiferromagnetic Spin $1/2$ Ladders

Spectral densities are computed in unprecedented detail for quantum antiferromagnetic spin $1/2$ two-leg ladders. These results were obtained due to a major methodical advance achieved by optimally chosen unitary transformations. The approach is based on dressed integer excitations. Considerable weight is found at high energies in the two-particle sector. Precursors of fractional spinon physics occur supporting the conclusion that there is no necessity to resort to fractional excitations in order to describe features at higher energies.