Strongly-entangled topological matter

点击翻译按钮获取中文摘要

This project will advance the theoretical understanding of the new type of matter called topological matter, which emerges in strongly-interacting quantum systems. By performing numerical simulations, the project will investigate fundamental properties of topological matter, such as its geometry and quantum entanglement. This will provide feedback to experiments on how to realise new topological matter in materials like bilayer graphene.Topology is a branch of mathematics that describes properties of objects which do not change under local perturbations. For example, a soccer ball is the same as a rugby ball because we can slowly stretch one into the other. Curiously, in certain semiconductor materials (like the ones used to build transistors and solar cells) there are phases of matter which are also insensitive to local perturbations. This topological matter is very different from ordinary matter (like water or ice) because it represents a collective state that emerges when many quantum particles interact, similar to superfluids and superconductors. Topological matter forms a very active field of modern condensed matter physics, for at least three reasons. First, topological matter has been seen in many beautiful experiments, starting with the original discovery of the fractional quantum Hall effect in the 1980s. Second, topological matter represents a major challenge for theoretical physics, because it cannot be explained by traditional solid state theories based on "symmetry breaking". Third, topological phases have very rich and unexpected properties, for example their low-energy excitations behave as "quasiparticles" which are more general than the Standard Model of particle physics (i.e., they are neither bosons nor fermions). Recent discovery of one such quasiparticle - the "Majorana fermion" - has attracted much public attention, and current research focuses on harnessing the power of the Majoranas to perform quantum computing. Thus, topological matter may have an important role to play in future quantum technologies. This project will advance the understanding of topological matter in the systems of strongly interacting particles, where many fundamental problems remain open. The project will investigate the role of geometry in topological matter, which determines their elastic and thermal properties. Furthermore, the project will investigate quantum correlations ("entanglement") in topological matter, with the goal of understanding how topological order could be enabled to survive at high temperatures. This would represent an important practical advance as most of topological matter is currently realised only at cryogenic conditions. Finally, the project will establish close connection to experiments that seek to realise topological matter in new materials. By developing and applying new numerical algorithms, the project will identify interaction-driven topological phenomena that can be experimentally accessed in bilayer graphene, in particular the phases that host the Majorana fermions or even more exotic "parafermion" quasiparticles.