Dynamical structure factor for the alternating Heisenberg chain: A linked cluster calculation

We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high-order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit (lambda=0), where complete wave vector and frequency-dependent spectral weights for one- and two-particle excitations (continuum and bound states) are obtained. For small to moderate values of the interdimer coupling parameter lambda, these lead to extremely accurate calculations of the dynamical structure factors. We also examine the variation of the relative spectral weights of one- and two-particle states with bond alternation all the way up to the limit of the uniform chain (lambda=1). In agreement with Schmidt and Uhrig, we find that the spectral weight is dominated by 2-triplet states even at lambda=1, which implies that a description in terms of triplet-pair excitations remains a good quantitative description of the system even for the uniform chain.