Title: Effect of collective spin excitation on electronic transport in topological spin texture

Abstract: We develop an efficient real-time simulation method for the spin-charge coupled system in the velocity gauge. This method enables us to compute the real-time simulation for the two-dimensional system with the complex spin texture. We focus on the effect of the collective excitation of the localized spins on the electronic transport properties of the non-trivial topological state in real space. To investigate this effect, we calculate the linear optical conductivity by calculating the real-time evolution of the Kondo lattice model on the triangular lattice, which hosts an all-in/all-out magnetic structure. In the linear conductivity spectra, we observe multiple peaks below the bandgap regime, attributed to the resonant contributions of collective modes similar to the skyrmionic system, alongside broadband modifications resulting from off-resonant spin dynamics. The result shows that the collective excitation, similar to the skyrmionic system, influences the optical response of the electron systems based on symmetry analysis. We elucidate the interference between the contributions from the different spin excitations to the optical conductivity in the multiple spin texture, pointing out the mode-dependent electrical activity. We show the complex interplay between the complex spin texture and the itinerant electrons in the two-dimensional spin-charge coupled system.