Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model

Abstract

We derive analytical results on energy spectral phase transitions and deformations in the simplest model of one-dimensional lattice displaying the non-Hermitian skin effect, namely the Hatano-Nelson model with unidirectional hopping, under on-site potential uncorrelated disorder in complex energy plane. While the energy spectrum under open boundary conditions (OBC) exactly reproduces the distribution of on-site potential disorder, the energy spectrum under periodic boundary conditions (PBC) undergoes spectral deformations, from one or more closed loops in the fully delocalized phase, with no overlap with the OBC spectrum, to a mixed spectrum (closed loops and some OBC energies) in the mobility edge phase, to a complete collapse toward the OBC spectrum in the bulk localized phase. Such transitions are observed as the strength of disorder is increased. Depending on the kind of disorder, different interesting behaviors are found. In particular, for continuous disorder with a radial distribution in complex energy plane it is shown that in the delocalized phase the energy spectrum under PBC is locked and fully insensitive to disorder, while transition to the bulk localized phase is signaled by the change of a topological winding number. When the disorder is described by a discrete distribution, the bulk localization transition never occurs, while topological phase transitions associated to PBC energy spectral splittings can be observed.

13 pages, 6 figures

References in corpus (14)

• 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
• Topological Transition in a Non-Hermitian Quantum Walk
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• New topological invariants in non-Hermitian systems
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Light Localization induced by Random Imaginary Permittivities
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition

Cited by in corpus (28)

• Topological Non-Hermitian skin effect
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian skin effect beyond the tight-binding models
• Non-Hermitian skin effect as an impurity problem
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Anderson localization versus hopping asymmetry in a disordered lattice
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Non-Hermitian control of localization in mosaic photonic lattices
• Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
• Field Theoretical Study of Disorder in Non-Hermitian Topological Models
• Phase transitions in non-Hermitian superlattices
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Recent progress on disorder-induced topological phases
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Dark solitons in nonlinear Su-Schrieffer-Heeger lattices
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal