  Nonlinear responses in condensed matter are intensively studied because they
provide rich information about materials and hold the possibility of being
applied in diodes or high-frequency optical devices. While nonlinear responses
in noninteracting models have been explored widely, the effect of strong
correlations on the nonlinear response is still poorly understood, even though
it has been suggested that correlations can enhance the nonlinear response. In
this work, we first give an analytical derivation of nonlinear responses using
the Green's function methods at finite temperature. Then, we discuss the
difficulties of considering dissipation using conventional methods, such as the
reduced density matrix method. We reveal that the relaxation time approximation
leads to severe limitations when considering optical responses. Finally, we
demonstrate that correlation effects, such as the renormalization of the band
structure and different lifetime in orbitals or sublattices, can significantly
enhance nonlinear responses and can even change the sign of the nonlinear
conductivity.
