Exploring phases of quantum matter with supersymmetry, holography and entanglement entropy

 Strongly interacting quantum matter still largely defies our theoretical understanding. Experiments on heavy fermion compounds, high-temperature superconductors and various organic materials have revealed phases with many properties that lack a theoretical explanation. Moreover, theoretical examples of phases of highly entangled, strongly interacting quantum matter are few and far between. These facts combined present the exciting possibility that we have only scratched the surface of what the quantum world has to offer. 

In this talk I will discuss three novel techniques that have recently started to show their power for studying highly entangled, strongly interacting quantum matter: supersymmetry, holography and entanglement entropy. Supersymmetric models for lattice fermions and holographic duality are both new frameworks that allow us to gain analytical control over strongly correlated systems. Entanglement entropy serves as a universal tool to give insight in the structure of phases of quantum matter.