Abstract
Spectral densities are calculated for the dimerized and frustrated $S=1/2$ 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 $S=1$ sector and for optical experiments (Raman scattering, infrared absorption) probing the $S=0$ 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.
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