Abstract

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path toward the constructive design of robust, long-range entangled many-body systems. Most recent theories unveil that non-trivial topology is crucially manifested in the zeros of the fermionic Green’s function in Mott insulating systems and demonstrate the occurrence of topological band structures of zeros, and – by bulk-boundary correspondence – of topological edge states of zeros [1]. In this talk, I will spend some time discussing the physical meaning of Green's function zeros and potential ways to probe them. I will then spend most of the time presenting an exactly soluble local model Hamiltonian [2]. I'll demonstrate the appearance of Green’s function zeros in a non-trivial, integrable limit of the model and employ controlled perturbation theory to demonstrate their topological band structure. An infinite order resummation of diagrams further allows to access the vicinity of the (topological) phase transition, and I'll demonstrate that Green’s function zeros acquire a finite lifetime. The local nature of the model allows us to straightforwardly calculate the quantized Hall response.

[1] N. Wagner, ..., EJK, ..., G. Sangiovanni, Nat Commun 14, 7531 (2023).
[2] S. Bollmann, C. Setty, U. Seifert, EJK arXiv:2312.14926