Spectral properties of the dimerized and frustrated $S=1/2\mathrm{}$ chain

Spectral densities are calculated for the dimerized and frustrated $S=1/2\mathrm{}$ chain using the method of continuous unitary transformations. The transformation to an effective triplon model is realized in a perturbative fashion up to high orders about the limit of isolated dimers. An efficient description in terms of triplons (elementary triplets) is possible: a detailed analysis of the spectral densities is provided for strong and intermediate dimerization including the influence of frustration. Precise predictions are made for inelastic neutron scattering experiments probing the $S=1\mathrm{}$ sector and for optical experiments (Raman scattering, infrared absorption) probing the $S=0\mathrm{}$ sector. Bound states and resonances influence the important continua strongly. The comparison with the field theoretic results reveals that the sine-Gordon model describes the low-energy features for strong to intermediate dimerization only at critical frustration.