Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect

Abstract

Non-Hermitian non-reciprocal systems are known to be extremely sensitive to boundary conditions, exhibiting diverse localizing behaviors and spectrum structures when translational invariance is locally broken, either by tuning the boundary coupling strength, or by introducing an effective boundary using impurities or defects. In this work, we consider the single impurity problem in the Hatano-Nelson model and the Su-Schreieffer-Heeger model, which can be exactly solved with the single impurity being treated as an effective boundary of the system. From our exact solutions for finite-size systems, we unveil that increasing the impurity strength can lead to a transition of the bulk states from non-skin states to skin states, accompanied by the change of the spectrum structure from an ellipse in the complex plane to a segment along the real axis. These exact results indicate that the critical value of impurity strength is size-dependent, and increases exponentially with the lattice size when the impurity is strong or the system is large enough. OUr exact solutions are also useful for determining the point-gap topological transition in the concerned models.

arXiv comment9 pages and 8 figures in total. Comments are welcome

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• Topological Non-Hermitian skin effect
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Accumulation of scale-free localized states induced by local non-Hermiticity
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Non-Hermitian boundary spectral winding
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Exact analogue of the Hatano-Nelson model in 1D continuous nonreciprocal systems
• Direction reversal of non-Hermitian skin effect via coherent coupling
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
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• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Localized states and skin effect around non-Hermitian impurities in tight-binding models
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• Nontrivial worldline winding in non-Hermitian quantum systems
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• Anomalous hybridization of spectral winding topology in quantized steady-state responses
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• Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems