Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
arXiv:2310.03412 · doi:10.1103/PhysRevE.109.044315
Abstract
We studied the single-particle Anderson localization problem for non-Hermitian systems on directed graphs. Random regular graph and various undirected standard random graph models were modified by controlling reciprocity and hopping asymmetry parameters. We found the emergence of left, biorthogonal and right localized states depending on both parameters and graph structure properties such as node degree . For directed random graphs, the occurrence of biorthogonal localization near exceptional points is described analytically and numerically. The clustering of localized states near the center of the spectrum and the corresponding mobility edge for left and right states are shown numerically. Structural features responsible for localization, such as topologically invariant nodes or drains and sources, were also described. Considering the diagonal disorder, we observed the disappearance of localization dependence on reciprocity around for a random regular graph . With a small diagonal disorder, the average biorthogonal fractal dimension drastically reduces. Around localization scars occur within the spectrum, alternating as vertical bands of clustering of left and right localized states.
arXiv comment15 pages, 8 figures
References in corpus (48)
- Emergence of scaling in random networks
- Edge states and topological invariants of non-Hermitian systems
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Localization transitions in non-Hermitian quantum mechanics
- Topological phases of non-Hermitian systems
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Spectral redemption: clustering sparse networks
- Vortex Pinning and Non-Hermitian Quantum Mechanics
- Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
- Biorthogonal Quantum Mechanics
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Non-Hermitian topological phenomena: A review
- Localization and centrality in networks
- Non-Hermitian Delocalization and Eigenfunctions
- Non-Hermitian Many-Body Localization
- Anderson localization on the Bethe lattice: non-ergodicity of extended states
- Characterizing the dynamical importance of network nodes and links
- Disorder-Free Localization
- Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Anderson localization on random regular graphs
- Non-Hermitian disorder in two-dimensional optical lattices
- Anderson transition in three-dimensional systems with non-Hermitian disorder
- Distinct types of eigenvector localization in networks
- Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
- From Anderson localization on Random Regular Graphs to Many-Body localization
- A single defect approximation for localized states on random lattices
- Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
- Non-Hermitian Many-Body Localization with Open Boundaries
- Anderson transition on the Bethe lattice: an approach with real energies
- Spectral Theory of Sparse Non-Hermitian Random Matrices
- Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
- Spectra of sparse non-Hermitian random matrices: an analytical solution
- Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
- Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure
- Spacing ratio characterization of the spectra of directed random networks
- The critical point of k-clique percolation in the Erdos-Renyi graph
- Topology in non-Hermitian Chern insulators with skin effect
- Localization and universality of eigenvectors in directed random graphs
- Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
- Renormalization to localization without a small parameter
- Algorithmic detectability threshold of the stochastic block model
- Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
- Quasiperiodicity hinders ergodic Floquet eigenstates
- Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
- Paths counting on simple graphs: from escape to localization
- Robust extended states in Anderson model on partially disordered random regular graphs