Series Expansions for Excited States of Quantum Lattice Models

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the Fourier series coefficients of elementary excitation spectra are directly obtained. The numerical calculations involved are straightforward extensions of those which have already been used to calculate series expansions for ground-state correlations and $T=0$ susceptibilities in a wide variety of models. As a test, we have reproduced the known elementary excitation spectrum of the transverse-field Ising chain in its disordered phase.