Transport properties of the Hubbard model within the dynamical mean-field theory

Abstract: While transport measurements (e.g. resistivity, Hall angle) are a routine characterization procedure for strongly correlated materials, it is quite difficult to reliably calculate the transport properties of the corresponding models in the experimentally relevant temperature range. In the past 25 years, the dynamical mean field theory was established as an approximation technique that is believed to capture many characteristic effects of the paradigmatic model for correlated compounds, the Hubbard model, in particular the physics of Mott metal-insulator transition. The approach becomes exact in the limit of infinite dimensions where it provides an exact mapping from the full lattice model to a self-consistently defined effective quantum impurity model, the single-impurity Anderson model. In this same limit, there are no vertex corrections and the conductivity can be computed knowing solely the impurity self-energy. Surprisingly, despite much effort, accurate results for the transport properties of the Hubbard model in all temperature regimes have become available only very recently through developments in numerical impurity solvers, such as the continuous-time quantum Monte Carlo and the numerical renormalization group. After discussing some technical aspects of the problem, I will present the current understanding of the various temperature regimes of the doped Mott insulator which are characterized by different transport behavior: Fermi-liquid, strange-metal, bad-metal, and the asymptotic linear-resistivity regime