Nonlinear response in Mott Insulators

We develop a new formalism to calculate linear and nonlinear response functions for a Mott insulator, with and without spin orbit coupling. We consider the effects of an external frequency dependent gauge field, within minimal coupling, on the fermionic degrees of freedom in the repulsive Fermi Hubbard model. This formalism is necessary for large onsite Hubbard interactions, since localized spin moments do not couple to an external electric field. We calculate the nonlinear photogalvanic effect and second harmonic generation, that are sensitive to underlying symmetries of materials. Our formalism allows us to highlight experimental signatures of symmetries and topology in spin orbit induced frustrated systems through the structure of the response tensors.