Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class

Abstract

Non-Hermitian Hamiltonians are generally sensitive to boundary conditions, and their spectra and wave functions under open boundary conditions are not necessarily predicted by the Bloch band theory for periodic boundary conditions. To elucidate such a non-Bloch feature, recent works have developed a non-Bloch band theory that works even under arbitrary boundary conditions. Here, it is demonstrated that the standard non-Bloch band theory breaks down in the symplectic class, in which non-Hermitian Hamiltonians exhibit Kramers degeneracy because of reciprocity. Instead, a modified non-Bloch band theory for the symplectic class is developed in a general manner, as well as illustrative examples. This nonstandard non-Bloch band theory underlies the ${\mathbb{Z}}_2$ non-Hermitian skin effect protected by reciprocity.

13 pages, 2 figures

References in corpus (16)

• Classification of topological insulators and superconductors in three spatial dimensions
• Exceptional Topology of Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological Transition in a Non-Hermitian Quantum Walk
• Critical non-Hermitian Skin Effect
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Active topological photonics
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Non-Bloch band collapse and chiral Zener tunneling
• Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions

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• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
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