Non-Hermitian physics: Exceptional points, symmetry and breakdown of the bulk-boundary correspondence

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 break down 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, and study the appearance of exceptional points in the presence of symmetries. Additionally, 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.