Extensions of dynamical mean-field theory to non-local correlations and multi-band systems

We have shown the importance and necessity of the inclusion of non-local correlations in the standard dynamical mean-field theory (DMFT) by the TRILEX study of the hole-doped adadom surface systems. Furthermore, the essential roles of the long-range interaction and lattice symmetry in triggering the superconducting pairing are revealed by analyzing the momentum resolved response functions. In order to include non-local correlations in the cluster extensions of DMFT and also handle multi-band systems, we move on to develop efficient impurity solver which lies at the core of DMFT calculations. By rotating to the natural-orbital basis, a projection framework on both frequency- and time-domain are proposed and tested. Furthermore, to counter the intrinsic difficulties of the MPS representation of the many-body wave function of a multi-band system, we have proposed a tree tensor-product states to capture the entanglement structures of multi-band models correctly. This solver has been tested by solving the prototypical SrVO3 and shows great potential for further applications