  Nonlinear responses in crystalline solids are attracting a great deal of
attention because of exciting phenomena, such as the bulk photovoltaic effect
in noncentrosymmetric crystals and the third harmonic generation related to
Higgs modes in superconductors, and their potential applicability to electronic
devices. Recently, nonlinear responses have also been studied in strongly
correlated electron systems. Experimental evidence has revealed that
correlations play a significant role in nonlinear responses. However, most
theoretical calculations only consider excitonic effects or involve numerically
demanding approaches, making interpreting the results challenging. In this
paper, we adopt another approach, which is based on real-time evolution using
the correlation expansion method. Particularly, we focus on the 1d interacting
Rice-Mele model. We analyze the impact of the density-density interaction on
the linear and nonlinear conductivities and demonstrate that two-particle
correlations beyond the mean-field level enhance second-order nonlinear
responses, especially the second harmonic generation, while the linear response
is not strongly affected. Furthermore, by decomposing the current into a
one-particle contribution and six two-particle contributions, we show that the
``biexciton transition" term and its nonlinear oscillations is the most
dominant two-particle contribution to the nonlinear response. In addition, we
also show that the intercell charge-charge correlation is strongly enhanced
when the system is driven with the frequency corresponding to the excitonic
peak and can even exceed the intracell correlation. This implies the
possibility of manipulating two-particle correlations with external fields.
