  Photoexcited states are relaxed by transferring energy to the environments.
In order to study which coupling allows fast energy transfer to lattice
vibrations in correlated electron systems, we calculate the time evolutions of
the kinetic energies of different types and frequencies of lattice vibrations.
The one-dimensional half-filled Hubbard model is augmented with
electron-lattice couplings that modulate transfer integrals, site energies, and
Coulomb repulsion strengths. The time-dependent Schr\"odinger equation is
solved for exact many-electron wave functions, and the classical equation of
motion for the lattice displacements. In order to transfer energy to classical
lattice vibrations that modulate transfer integrals or site energies, the
translational invariance must be broken to give optical activity to an
electronic excitation with wave number $ \pi $ and to these lattice vibrations.
On the other hand, a certain amount of energy is always transferred to lattice
vibrations that modulate Coulomb repulsion strengths, irrespective of the
symmetry of the ground state, as long as the corresponding electron-lattice
couplings are present. In strongly correlated electron systems, these couplings
can be strong, although they are usually insignificant because their effects on
the equilibrium properties can be absorbed into redefinition of Coulomb
repulsion strengths. We will discuss competition or collaboration between
energy transfer pathways through different types of electron-lattice couplings.
