  The disclosure of basic nonlinear optical properties of graphene-like
nanostructures with correlated electron-hole nonlinear dynamics over a wide
range of frequencies and pump field intensities is of great importance for both
graphene fundamental physics and for expected novel applications of 2D
hexagonal nanostructures in extreme nonlinear optics. In the current paper, the
nonlinear interaction of 2D hexagonal nanostructures with the bichromatic
infrared driving field taking into account many-body Coulomb interaction is
investigated. Numerical investigation in the scope of the Bloch equations
within the Houston basis that take into account $e-e$ and $e-h$ interactions in
the Hartree-Fock approximation reveals significant excitonic effects in the
high harmonic generation process in 2D hexagonal nanostructures such as
graphene and silicene. It is shown that due to the correlated electron-hole
nonlinear dynamics around the van Hove singularity, spectral caustics in the
high harmonic generation spectrum are induced near the saddle point excitonic
resonances.
