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Spin Seebeck coefficient and spin-thermal diffusion in the two-dimensional Hubbard model

We investigate the spin Seebeck coefficient $S_s$ in the square lattice Hubbard model at high temperatures of relevance to cold-atom measurements. We solve the model with the finite-temperature Lanczos and with the dynamical mean-field theory methods and find they give similar results in the considered regime. $S_s$ exceeds the atomic 'Heikes' estimates and the Kelvin entropic estimates drastically. We analyze the behavior in terms of a mapping onto the problem of a doped attractive model and derive an approximate expression that allows relating the enhancement of $S_s$ to distinct scattering of the spin-majority and the spin-minority excitations. Our analysis reveals the limitations of entropic interpretations of Seebeck coefficient even in the high-temperature regime. Large values of $S_s$ could be observed on optical lattices. We also calculate the full diffusion matrix. We quantify the spin-thermal diffusion, that is, the extent of the mixing between the spin and the thermal diffusion and discuss the results in the context of recent measurements of the spin-diffusion constant in cold atoms.