Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions

Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each other. Comparing Green functions for periodic and open boundary conditions we find that, in general, there is no correspondence between topological invariants computed for periodic boundary conditions, and boundary eigenstates observed for open boundary conditions. Instead, we find that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.

Automated summary

This study investigates the realization of genuinely non-Hermitian topological phases in open systems with strong gain and loss, and reveals that the non-Hermitian winding number in one dimension indicates a topological phase transition in the bulk, implying spatial growth of the bulk Green function.