Thermal conductivity and heat diffusion in the two-dimensional Hubbard model

We study the electronic thermal conductivity $\kappa_\textrm{el}$ and the thermal diffusion constant $D_\textrm{Q,el}$ in the square lattice Hubbard model using the finite-temperature Lanczos method. We exploit the Nernst-Einstein relation for thermal transport and interpret the strong non-monotonous temperature dependence of $\kappa_\textrm{el}$ in terms of that of $D_\textrm{Q,el}$ and the electronic specific heat $c_\textrm{el}$. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that $\kappa_\textrm{el}$ is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above or close to lattice spacing. We discuss the opposite effect of quasi-particle renormalization on charge and heat diffusion constants. We calculate the Lorenz ratio and show that it differs from the Sommerfeld value. We discuss our results in relation to experiments on cuprates. Additionally, we calculate the thermal conductivity of overdoped cuprates within the anisotropic marginal Fermi liquid phenomenological approach.