"Zero is Not Nothing: Correlated topological ground states and quantum circuits"
Prof. Elio König
University of Wisconsin-Madison

Live streaming: Zoom link

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 present 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 access to 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. Finally, I will discuss a unitary quantum circuit emulating the phenomenon of topological Green's function zeros. Crucially, this corresponds to a Floquet case in which zeros of the Green's function occur even in the non-interacting limit (matchgate circuits). Non-trivial topological Green's function zeros can be further induced by a generalization of the mechanism of symmetric mass generation [3].

[1] N. Wagner, ..., EJK, T. Schäfer, ..., G. Sangiovanni, Nat Commun 14, 7531 (2023)
[2] S. Bollmann, C. Setty, U. Seifert, EJK, PRL 133 (13), 136504
[3] EJK, A Mitra, in preparation.