Multiscale approaches to strongly correlated systems in and out of equilibrium

The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, many of the mechanisms responsible for these technologically promising properties remain rather elusive. Computational approaches have played a major role in helping to fill this void. In particular, dynamical mean field theory (DMFT) and its cluster extension, the dynamical cluster approximation (DCA) have allowed significant progress. However, despite all the insightful results of the dynamical cluster approximation, computational constraints (sign problem, exponential growth of the Hilbert space) still limit the length scale within which correlation can be treated exactly in the formalism. A natural next step is the development of multiscale many body approaches whereby this challenge is addressed by introducing, between the short length scale where correlations are treated exactly using a cluster solver such Quantum Monte Carlo (QMC) or exact diagonalization, and the long length scale where correlations are treated in a mean field, an intermediate length scale within which correlations can be treated perturbatively. We will discuss implementations of this multiscale many body approach, the results they have yielded and some challenges that persist. In addition, we will discuss the framework for extension of the quantum cluster approximations to the nonequilibrium problem.