Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
arXiv:2502.14199 · doi:10.1103/PhysRevB.111.L140201
Abstract
Scale-free localization emerging in non-Hermitian physics has recently garnered significant attention. In this work, we explore the interplay between scale-free localization and Anderson localization by investigating a unidirectional quasiperiodic model with generalized boundary conditions. We derive analytical expressions of Lyapunov exponent from the bulk equations. Together with the boundary equation, we can determine properties of eigenstates and spectrum and establish their exact relationships with the quasiperiodic potential strength and boundary parameter. While eigenstates exhibit scale-free localization in the weak disorder regime, they become localized in the strong disorder regime. The scale-free and Anderson localized states satisfy the boundary equation in distinct ways, leading to different localization properties and scaling behaviors. Generalizing our framework, we design a model with exact energy edges separating the scale-free and Anderson localized states via the mosaic modulation of quasiperiodic potentials. Our models can be realized experimentally in electric circuits.
References in corpus (52)
- Edge states and topological invariants of non-Hermitian systems
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Topological Origin of Non-Hermitian Skin Effects
- Anomalous edge state in a non-Hermitian lattice
- Non-Bloch Band Theory of Non-Hermitian Systems
- Correspondence between winding numbers and skin modes in non-hermitian systems
- Non-Hermitian Boundary Modes
- Anatomy of skin modes and topology in non-Hermitian systems
- Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
- Critical non-Hermitian Skin Effect
- Topological phase transition in non-Hermitian quasicrystals
- Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
- One dimensional quasiperiodic mosaic lattice with exact mobility edges
- Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
- Topological Phases in Non-Hermitian Aubry-André-Harper Models
- Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
- Skin effect and winding number in disordered non-Hermitian systems
- Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
- Simulating non-Hermitian quasicrystals with single-photon quantum walks
- Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
- Exact mobility edges, -symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
- Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
- Impurity induced scale-free localization
- Nonunitary Scaling Theory of Non-Hermitian Localization
- Many-body localization in a non-Hermitian quasi-periodic system
- Phase transitions in a non-Hermitian Aubry-André-Harper model
- Localization and topological transitions in non-Hermitian quasiperiodic lattices
- Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
- Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
- Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
- Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
- Accumulation of scale-free localized states induced by local non-Hermiticity
- Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
- Scale-free localization and PT symmetry breaking from local non-Hermiticity
- Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
- Non-Hermitian spectra and Anderson localization
- Scale-tailored localization and its observation in non-Hermitian electrical circuits
- Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
- Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
- Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
- Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
- Exact mobility edges for 1D quasiperiodic models
- Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
- Observation of scale-free localized states induced by non-Hermitian defects
- Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
- Universal scalefree non-Hermitian skin effect near the Bloch point
- Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
- Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
- Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
- Observation of size-dependent boundary effects in non-Hermitian electric circuits
- From scale-free to Anderson localization: a size-dependent transition
- Lack of near-sightedness principle in non-Hermitian systems