Abstract

Recent experimental progress enables the study of strongly interacting systems which are driven to exotic quantum states by strong external fields. Examples include cold gases of Rydberg atoms with strong dipole-dipole interactions and organic salts where valence electrons are coupled to localized molecular vibrations. In both cases equilibration takes much longer than the duration of the pump pulses and insights into the physics can therefore be gained by considering purely coherent evolution away from their initial equilibrium state. In this talk I will first present the method of Path-Sums which allows to efficiently evaluate matrix functions, and show how we apply it to determining long-range diagonal and off-diagonal order through Rydberg blockade and anti-blockade in ultracold atomic ensembles. I will then introduce Tensor Network Theory which is based on insights into the properties and scaling of entanglement and discuss how we use it to describe the coherent evolution of a Hubbard model which accurately describes the physics of the organic salt (BEDT-TTF)-F2TCNQ at room temperature, thus indicating quantum coherent electron dynamics.