State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems

Abstract

The breakdown of the bulk-boundary correspondence in non-Hermitian (NH) topological systems is an open, controversial issue. In this paper, to resolve this issue, we ask the following question: Can a (global) topological invariant completely describe the topological properties of a NH system as its Hermitian counterpart? Our answer is no. One cannot use a global topological invariant (including non-Bloch topological invariant) to accurately characterize the topological properties of the NH systems. Instead, there exist a new type of topological invariants that are absence in its Hermitian counterpart -- the state dependent topological invariants. With the help of the state-dependent topological invariants, we develop a new topological theory for NH topological system beyond the general knowledge for usual Hermitian systems and obtain an exact formulation of the bulk-boundary correspondence, including state-dependent phase diagram, state-dependent phase transition and anomalous transport properties (spontaneous topological current). Therefore, these results will help people to understand the exotic topological properties of various non-Hermitian systems.

arXiv comment6 pages, 2 figures

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Cited by in corpus (3)

• Non-Hermitian Chiral Skin Effect
• Entanglement Entropy of Non-Hermitian Free Fermions
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence