  Nonlinear responses give rise to various exciting phenomena, which are
forbidden in linear responses. Among them, one of the most fascinating
phenomena is the recently observed giant spontaneous Hall effect in
$\mathrm{Ce_{3}Bi_{4}Pd_{3}}$. This material is a promising candidate for a
Weyl-Kondo semimetal, and this experiment implies that strong correlation
effects can enhance the nonlinear Hall effect. However, most theoretical
studies on nonlinear responses have been limited to free systems, and the
connection between nonlinear responses and strong correlation effects is poorly
understood. Motivated by these experiments and recent theoretical advances to
analyze strong correlation effects on the nonlinear response, we study a
periodic Anderson model describing $\mathrm{Ce_{3}Bi_{4}Pd_{3}}$ using the
dynamical mean-field theory. We calculate the nonlinear longitudinal
conductivity and the nonlinear Hall conductivity using the Kubo formula
extended to the nonlinear response regime and clarify their temperature
dependences. We numerically show that strong correlations can enhance nonlinear
conductivities, and we conclude that the magnitude of the experimentally
observed giant nonlinear Hall effect can be explained by strong correlation
effects.
