Quantum Monte Carlo impurity solvers for multi-orbital problems and frequency-dependent interactions

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Modern methods to describe and predict properties of materials with strong electronic correlations rely on a combination of density functional and dynamical mean-field theories. This approach reduces a fermionic lattice problem to the self-consistent solution of a quantum impurity model and, thus, relies on efficient methods to solve impurity problems. These so-called impurity solvers constitute the core of this research project. In recent years, we have witnessed breakthroughs in this domain with the development of continuous time (diagrammatic) quantum Monte Carlo approaches as well as a multigrid formulation of the well-known Hirsch-Fye algorithm. The diagrammatic Monte Carlo methods can be applied to multiorbital systems with the full rotationally invariant Coulomb interactions and, thus, appear suitable for the study of transition metal and actinide compounds. One purpose of this project is to compare the performance of the different Monte Carlo approaches, to establish the parameter regimes in which they work most efficiently, and to study the effect of previously neglected interactions. The second purpose is to extend the continuous-time impurity solvers to frequency-dependent (screened) interactions, which are expected to be relevant for a quantitative description of some transition metal compounds.