  By employing the exact diagonalization method, we investigate the
high-harmonic generation (HHG) of the correlated systems under the strong laser
irradiation. For the extended Hubbard model on a periodic chain, HHG close to
the quantum critical point (QCP) is more significant compared to two
neighboring gapped phases (i.e., charge-density-wave and spin-density wave
states), especially in low-frequencies. We confirm that the systems in the
vicinity of the QCP are supersensitive to the external field and more
optical-transition channels via excited states are responsible for HHG. This
feature holds the potential of obtaining high-efficiency harmonics by making
use of materials approaching to QCP. Based on two-dimensional Haldane model, we
further propose that the even- or odd-order components of generated harmonics
can be promisingly regarded as spectral signals to distinguish the
topologically ordered phases from locally ordered ones. Our findings in this
work pave the way to achieve ultrafast light source from HHG in strongly
correlated materials and to study quantum phase transition by nonlinear optics
in strong laser fields.
