Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems

Abstract

The consistency between eigenvalues calculated under open and periodic boundary conditions, named as {\it bulk-bulk correspondence} ($\mathcal{BBC}$), can be destroyed in systems with non-Hermitian skin effect (NHSE). In spite of the great success of the generalized Brillouin zone (GBZ) theory in clean non-Hermitian systems, the applicability of GBZ theory is questionable when the translational symmetry is broken. Thus, it is of great value to rebuild the $\mathcal{BBC}$ for disorder samples, which extends the application of GBZ theory in non-Hermitian systems. Here, we propose a scheme reconstructing $\mathcal{BBC}$, which can be regarded as the solution of an optimization problem. By solving this optimization problem analytically, we reconstruct the $\mathcal{BBC}$ and obtain the modified GBZ theory in several prototypical disordered non-Hermitian models. The modified GBZ theory gives a precise description of NHSE, which predicts the intriguing disorder-enhanced and disorder-irrelevant NHSEs.

5 pages, 3 figures, including Supplementary Materials

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Cited by in corpus (23)

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• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Observation of disorder-induced boundary localization
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Anomalous dynamical response of non-Hermitian topological phases
• From scale-free to Anderson localization: a size-dependent transition
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Topological spin textures in electronic non-Hermitian systems
• Recent progress on disorder-induced topological phases
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal