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We study how the synergetic effect of spin-orbit coupling (SOC) and Zeemansplitting (ZS) affects the optical conductivity in the one-dimensional Hubbardmodel using the Kubo formula. We focus on two phenomena: (1) the electricdipole spin resonance (EDSR) in the metallic regime and (2) the opticalconductivity in the Mott-insulating phase above the optical gap. In both cases,we calculate qualitatively the effects of SOC and ZS and how they depend on therelative angle between the SOC vector and the magnetic field direction. First,we investigate the spin resonance without electron correlation (the Hubbardparameter $U=0$). Although, neither SOC nor ZS causes any resonance by itselfin the optical conductivity, the EDSR becomes possible when both of them exist.The resulting contribution to the optical conductivity is analyzedanalytically. The effect of $U$ on the spin resonance is also studied with anumerical method. It is found that at half-filling, the resonance is firstenhanced for small $U$ and then suppressed when the optical gap is largeenough. In the strong coupling limit $U \rightarrow \infty$ at half-filling, wealso refer to the resonance between the lower and upper Hubbard bands appearingat $\omega \sim U$, above the optical gap. A large magnetic field tends tosuppress the signal while it is recovered thanks to SOC depending on therelative angle of the magnetic field.

Synergetic effect of spin-orbit coupling and Zeeman splitting on the optical conductivity in the one-dimensional Hubbard model