  We study high-harmonic generation (HHG) in the one-dimensional Hubbard model
in order to understand its relation to elementary excitations as well as the
similarities and differences to semiconductors. The simulations are based on
the infinite time-evolving block decimation (iTEBD) method and exact
diagonalization. We clarify that the HHG originates from the doublon-holon
recombination, and the scaling of the cutoff frequency is consistent with a
linear dependence on the external field. We demonstrate that the subcycle
features of the HHG can be reasonably described by a phenomenological three
step model for a doublon-holon pair. We argue that the HHG in the
one-dimensional Mott insulator is closely related to the dispersion of the
doublon-holon pair with respect to its relative momentum, which is not
necessarily captured by the single-particle spectrum due to the many-body
nature of the elementary excitations. For the comparison to semiconductors, we
introduce effective models obtained from the Schrieffer-Wolff transformation,
i.e. a strong-coupling expansion, which allows us to disentangle the different
processes involved in the Hubbard model: intraband dynamics of doublons and
holons, interband dipole excitations, and spin exchanges. These demonstrate the
formal similarity of the Mott system to the semiconductor models in the dipole
gauge, and reveal that the spin dynamics, which does not directly affect the
charge dynamics, can reduce the HHG intensity. We also show that the long-range
component of the intraband dipole moment has a substantial effect on the HHG
intensity, while the correlated hopping terms for the doublons and holons
essentially determine the shape of the HHG spectrum. A new numerical method to
evaluate single-particle spectra within the iTEBD method is also introduced.
