Laboratoire de Physique Théorique
Toulouse - UMR 5152

Topology and geometry help us understand many physical phenomena. Their broad applicability without resort to explicit parameters leads to a variety of simple universal behaviours. In this presentation, I will introduce some geometric effects in correlated electrons and topological effects in photonic band structures. In the first part, I will show how geometry of quantum states can help us understand electrons in flat bands. Such systems are dominated by interactions and host intriguing states with fractional statistics. I will show how nonuniform quantum distances between the Bloch states lead to emergent particle-hole asymmetry and serve as a guideline to the interacting phase diagram. This has several applications in twisted moiré systems. In the second part,I will go to my recent work on photonic bands, where dissipation can be modelled by simple non-Hermitian evolution. I will briefly introduce my recent classification. This leads to generic nodal points carrying non-Abelian charges and topology duality in quantum states. These phenomena are realised experimentally through a single-photon interferometry.