Dr. Flore Kunst from the Max Planck Institute for Quantum Optics
Title: Topology in non-Hermitian systems: Exceptional points, symmetry and the breakdown of the bulk-boundary correspondence.
Abstract: While topological phases of matter have mostly been studied for closed, Hermitian systems, a recent shift has been made towards considering these phases in the context of non-Hermitian Hamiltonians, which form a useful approach to describe dissipation. Such Hamiltonians may feature many exotic properties, which are radically different from their Hermitian counterparts, such as the generic appearance of exceptional points, a breakdown of the famed bulk-boundary correspondence, and the piling up of bulk states at the boundaries known as the non-Hermitian skin effect. In this talk, I will make use of two-band models to study these features in more detail. In particular, I will show that even though the conventional bulk-boundary correspondence breaks down, it is possible to define a biorthogonal bulk-boundary correspondence by making use of biorthogonal quantum mechanics. Additionally, I will introduce the concept of transfer matrices in the context of non-Hermitian physics, and discuss how the appearance of the aforementioned exotic properties can be straightforwardly understood in this language.