Matsubara-frequency-resolved spin exchange-correlation kernel for the three-dimensional uniform electron gas

The spin Coulomb drag effect, arising from the exchange of momentum between electrons of opposite spins, plays a crucial role in the spin transport of interacting electron systems and can be characterized by the exchange-correlation (XC) kernel in the spin channel ${K}_{\mathrm{XC}}^{\ensuremath{-}}(q,\ensuremath{\omega})$. Using the state-of-the-art variational diagrammatic Monte Carlo approach, we compute the Matsubara-frequency-resolved spin XC kernel ${K}_{\mathrm{XC}}^{\ensuremath{-}}(q,i{\ensuremath{\omega}}_{n})$ for the three-dimensional uniform electron gas at sufficiently low temperatures with high precision. In the long-wavelength limit, we identified a singular behavior of the form $A(i{\ensuremath{\omega}}_{n})/{q}^{2}$, confirming the theoretically predicted ultranonlocal behavior associated with spin Coulomb drag. Analysis of this structure in the low-frequency region enables precise determination of two crucial parameters characterizing the spin Coulomb drag effect: the spin mass enhancement factor and spin diffusion relaxation time. We observe a significant trend of increasing enhancement of the spin mass factor with decreasing electron density, and we provide clear evidence for the suppression of spin diffusion at low temperatures. These quantitative findings advance our understanding of Coulomb interaction effects on spin transport and provide essential parameters for time-dependent density functional theory and spintronics applications.