Why does bulk boundary correspondence fail in some non-hermitian topological models

Understand

Bulk boundary correspondence is crucial to topological insulator as it associates the boundary states (with zero energy, chiral or helical) to topological numbers defined in bulk.

• The application of this correspondence needs a prerequisite condition which is usually not mentioned explicitly: the boundaries themselves cannot alter the bulk states, so as to the topological numbers defined on them.
• In non-hermitian models with fractional winding number, we prove that such precondition fails and the bulk boundary correspondence is cut out.
• We show that, as eliminating the hopping between the boundaries to simulate the evolution of a system from the periodic boundary condition to the open boundary condition, exceptional points must be passed through and the topological structure of the spectrum has been changed.