Speaker
Description
We present recent developments in hierarchical representations of nonequilibrium Green’s functions, including applications and open challenges. We begin by comparing global iterative solvers, which suffer from error-front propagation, with time-stepping approaches that avoid this limitation. We show that hierarchical representations have become a practical tool for contemporary problems, including applications to driven superconducting and excitonic systems. Through the development of the open-source H-NESSi library, these methods are made accessible to the broader community. As a main application, we present transport calculations for the weakly interacting two-dimensional Hubbard model, where hierarchical time representations enable simulations of large lattices and calculations of the optical response and DC conductivity at very low temperatures. Preliminary results reveal a broad regime of linear resistivity at weak coupling, characteristic of strange-metal behaviour. We conclude with a discussion of the remaining challenges in extending these methods to realistic systems.