Excitation spectra and thermodynamic response of segmented Heisenberg spinchains

The spectral and thermodynamic response of segmented quantum spin chains is analyzed using a combination of numerical techniques and finite-size scali ng arguments. Various distributions of segment lengths are considered, incl uding the two extreme cases of quenched and annealed averages. As the impur ity concentration is increased, it is found that (i) the integrated spectra l weight is rapidly reduced, (ii) a pseudogap feature opens up at small fre quencies, and (iii) at larger frequencies a discrete peak structure emerges , dominated by the contributions of the smallest cluster segments. The corr esponding low-temperature thermodynamic response has a divergent contributi on due to the odd-site clusters and a subdominant exponentially activated c omponent due to the even-site segments whose finite-size gap is responsible for the spectral weight suppression at small frequencies. Based on simple scaling arguments, approximate low-temperature expressions are derived for the uniform susceptibility and the heat capacity. These are shown to be in good agreement with numerical solutions of the Bethe ansatz equations for e nsembles of open-end chains.