Questionable stability of dissipative topological models for classical and quantum systems

However, non-Hermitian Hamiltonians break with concepts that are known from energy-conserving systems such as the bulk-boundary correspondence (BBC) in these materials. This correspondence relates the topological properties of the bulk of the material to the physics of the edges. In the Hermitian case, the bulk of such a material can be described by neglecting the edges and just assuming the material to be infinite or periodic, since boundary effects do not affect the physics of the inside.

Surprisingly, this holds no longer true if the energy is not conserved: the properties of the boundary suddenly have a huge influence on the bulk system and subsequently have to be taken into account. It leads to a drastically altered BBC (bulk-boundary correspondence) for non-Hermitian systems. In particular, Koch and Budich studied different strengths of the coupling between boundaries and their effect on the bulk system. Knowing that in realistic quantum mechanical systems there is always an interaction between the edges -- admittedly an extremely small one -- they explored the extent to which decoupled edges are generally observable. Koch and Budich found that the spectrum of the topological material is stable under physically motivated perturbations such as the suppressed interactions between the boundaries.