  To elucidate different photoinduced melting dynamics of charge orders
observed in quasi-two-dimensional organic conductors $ \theta
$-(BEDT-TTF)$_2$RbZn(SCN)$_4$ and $ \alpha $-(BEDT-TTF)$_2$I$_3$
[BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene], we theoretically study
photoinduced time evolution of charge and spin correlation functions on the
basis of exact many-electron wave functions coupled with classical phonons in
extended Peierls-Hubbard models on anisotropic triangular lattices. In both
salts, the so-called horizontal-stripe charge order is stabilized by
nearest-neighbor repulsive interactions and by electron-lattice interactions.
In $ \theta $-(BEDT-TTF)$_2$RbZn(SCN)$_4$ (abbreviated as $ \theta $-RbZn), the
stabilization energy due to lattice distortion is larger, so that larger
quantity of energy needs to be absorbed for the melting of the charge and
lattice orders. The photoinduced charge dynamics shows a complex behavior owing
to a substantial number of nearly degenerate eigenstates involved. This is
related to the high structural symmetry when the lattice is undistorted. In $
\alpha $-(BEDT-TTF)$_2$I$_3$ (abbreviated as $ \alpha $-I$_3$), the lattice
stabilization energy is smaller, and smaller quantity of energy is sufficient
to melt the charge and lattice orders leading to a metallic phase. The
photoinduced charge dynamics shows a sinusoidal oscillation. In $ \alpha
$-I$_3$, the low structural symmetry ensures nearly spin-singlet bonds between
hole-rich sites, where the spin correlation survives even after
photoexcitation.
