  We explore the significance of laser-induced correlation effects for
high-order harmonic generation (HHG) in a linear chain model of a generic band
gap material for both single-IR-pulse and VUV-pump--IR-probe HHG schemes. We
examine various pump-pulse excitations, and catagorize signatures of
laser-induced correlation effects into two classes related to edge-state and
bulk-like effects. The relative importance of the edge-state effects decrease
with increasing system-size, while the bulk-like effects remain. We identify
regimes where these effects may alter the harmonic yield by an order of
magnitude, but also regions where they may be neglected. We characterize the
underlying laser-induced dynamics of the correlational mechanisms, using both
an electronic population-description in a static field-free basis, and
comparing to a bandstructure-picture with laser-induced time-dependent energy
shifts. From this we provide a guideline on when to account for laser-induced
electron correlations and give an estimate of the time-scale in which the
laser-induced electron-electron interactions can cause correlational changes in
the harmonic spectra. We find this timescale to be a few tens of femtoseconds.
