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

Abstract

We investigate the spin Seebeck coefficient Ss 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. Ss 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 Ss 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 Ss could be observed on optical lattices. We also calculated the full diffusion matrix. We quantified 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.