Quantum materials are on the rise and during last years there have been a large amount of predictions and discoveries of strongly correlated 2D materials, their ordered phases, and the vast possibilities to manipulate them various ways. These materials are often so called van der Waals crystals that can be “peeled” atomic layer by layer from a 3D bulk material down to a few or even a single crystal layer. The low dimensionality enables unprecedented possibilities to externally tune their properties by external knobs such as e.g. electrostatic gating, by combining them together in heterostructures, or by placing ad-atoms on their surface. Many 2D materials have complex phase diagrams with several competing ordered states at low temperatures as parameters such as e.g. carrier doping, pressure, or magnetic field are varied. The main purpose of this proposal is to study these materials and to develop theoretical and computational tools to describe their broken symmetry phases and the resulting phase diagrams. Furthermore we will study transport in heterostructures composed of 2D materials. New dressed states and new quasiparticle species follow from strong many-body effects and can be excited by applying pressure, electrostatic gating, magnetic or electrical fields or illuminating by light in the THZ to the infrared frequency range. Signatures thereof can be probed by different type of tunnelling probes and transport measurements.