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

Physical Review Letters
Heinrich-Gregor ZirnsteinBernd Rosenow

Abstract

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.

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Citations

Jul 3, 2021·Physical Review Letters·Li-Wei Yu, Dong-Ling Deng
Aug 24, 2021·Physical Review Letters·Xiao-Qi SunTaylor L Hughes
Sep 8, 2021·Nature Communications·Linhu LiJiangbin Gong

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