The past few years have seen a revived interest in quantum geometrical characterizations. Although the metric tensor has been connected to many geometrical concepts for single bands, the exploration of these concepts to a multi-band paradigm still promises a new field of interest. I will discuss a new route involving Pl\"ucker embeddings to represent arbitrary classifying spaces, being the essential objects that encode all the relevant topology for any multi-band system. While I will argue that this tool can be applied in contexts that range from response theories to finding quantum volumes and bounds on superfluid densities as well as possible quantum computations, I will in particular also show that they can be used to formulate projector Hamiltonians with projected entangled pair ground (PEPS) states that have a finite topological invariant, the Euler class, circumventing many no-go theorems. We further demonstrate the versatility of our model states by applying a shallow quantum circuit, producing interacting PEPS and simple parent Hamiltonians in the Euler phase. These model states moreover pinpoint to new interacting physics.
Professor Robert-Jan Slager obtained his doctorate (2016 with Professor Zaanen) and completed his undergraduate studies, which includes a master's degree in physics (2009 – 2011) and a double bachelor's degree in physics and mathematics (2006 – 2009), at Leiden University. These achievements have, amongst others, been recognised with a national Shell award from the Royal Holland Society of Science and Humanities and a cum laude distinction for his PhD, which involves a special evaluation of a committee of internationally acclaimed researchers and is awarded to approximately 5% of all doctorate students at the University. These studies were followed by postdoctoral positions at the Max Planck Institute for Complex systems and Harvard University, culminating in the acquisition of a principal investigator position at the Department of Physics, University of Cambridge. Per October 2024 he was then installed as Professor of Theoretical Physics at the University of Manchester.