Strongly-correlated quantum systems are often extremely fragile and notoriously hard to control, which poses challenges for possible technological applications. That is why a certain subclass of quantum states, the so-called topological phases of matter, recently attracted much attention. These are characterised by a certain degree of stability and robustness under perturbations, rooted in their special mathematical properties. Apriori, it is not always clear whether a given quantum state of matter is topological or not. We propose a mathematical criterion, which we call ''the geometric test", to tell whether a state of matter is in a topological phase. We then apply our test to strongly-interacting states of matter in Quantum Hall effect, observed in certain 2d materials (Gallium-arsenide, graphene, ...) at low temperatures and in strong magnetic fields. I will explain the idea of the test (which works pretty well) and the results, based on recent and upcoming works with Dimitri Zvonkine (Paris) and with Igor Burban (Paderborn).

https://meet.google.com/you-qymk-ybu