Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
arXiv:2204.00669 · doi:10.1103/PhysRevB.106.094204
Abstract
We study the stability of non-ergodic but extended (NEE) phases in non-Hermitian systems. For this purpose, we generalize a so-called Rosenzweig-Porter random-matrix ensemble (RP), known to carry a NEE phase along with the Anderson localized and ergodic ones, to the non-Hermitian case. We analyze, both analytically and numerically, the spectral and multifractal properties of the non-Hermitian case. We show that the ergodic and the localized phases are stable against the non-Hermitian nature of matrix entries. However, the stability of the fractal phase depends on the choice of the diagonal elements. For purely real or imaginary diagonal potential the fractal phases is intact, while for a generic complex diagonal potential the fractal phase disappears, giving the way to a localized one.
arXiv comment11 pages, 6 figures, 89 references
References in corpus (71)
- Nonequilibrium dynamics of closed interacting quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Edge states and topological invariants of non-Hermitian systems
- Anderson Transitions
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Localization transitions in non-Hermitian quantum mechanics
- The many-body localization phase transition
- Topological phases of non-Hermitian systems
- Topological Origin of Non-Hermitian Skin Effects
- Many-body localization edge in the random-field Heisenberg chain
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Phenomenology of fully many-body-localized systems
- A phenomenology of certain many-body-localized systems
- Non-Hermitian Boundary Modes
- Spawning rings of exceptional points out of Dirac cones
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Many-body localization: an introduction and selected topics
- On Many-Body Localization for Quantum Spin Chains
- Integrals of motion in the Many-Body localized phase
- Edge states and topological phases in non-Hermitian systems
- Topological Transition in a Non-Hermitian Quantum Walk
- Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
- Topologically protected midgap states in complex photonic lattices
- Non-Hermitian Many-Body Localization
- Multifractal Scalings across the Many-Body Localization Transition
- Ergodicity breaking in a model showing many-body localization
- Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
- A random matrix model with localization and ergodic transitions
- Non-Hermitean Random Matrix Theory: method of hermitization
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Eigenvector statistics in non-Hermitian random matrix ensembles
- Non-Hermitean Localization and De-Localization
- Operator scaling dimensions and multifractality at measurement-induced transitions
- Correlations of Nearby Levels Induced by a Random Potential
- Nonunitary Scaling Theory of Non-Hermitian Localization
- Non-Gaussian Non-Hermitean Random Matrix Theory: phase transitions and addition formalism
- Anderson transition in three-dimensional systems with non-Hermitian disorder
- Rare thermal bubbles at the many-body localization transition from the Fock space point of view
- From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
- Return probability for the Anderson model on the random regular graph
- The Many-Body localization transition in the Hilbert space
- Quantized conductance through a spin-selective atomic point contact
- Dynamical phases in a "multifractal" Rosenzweig-Porter model
- Eigenfunction distribution for the Rosenzweig-Porter model
- Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
- Sub-diffusion in the Anderson model on random regular graph
- Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
- Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
- The Lévy-Rosenzweig-Porter random matrix ensemble
- Spectral Theory of Sparse Non-Hermitian Random Matrices
- Multifractality without fine-tuning in a Floquet quasiperiodic chain
- Non-ergodic extended states in the SYK model
- Transition from Poisson to gaussian unitary statistics: The two-point correlation function
- Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
- Non-Hermitian spectra and Anderson localization
- Spatial and temporal localization of light in two dimensions
- Non-ergodic extended phase of the Quantum Random Energy model
- "Single Ring Theorem" and the Disk-Annulus Phase Transition
- Intensity fluctuations signature of 3D Anderson localization of light
- Critical statistics for non-Hermitian matrices
- Non-Hermiticity and Universality
- Quantum simulations of localization effects with dipolar interactions
- Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
- Anderson localization of light in dimension
Cited by in corpus (26)
- Non-ergodic delocalized phase with Poisson level statistics
- Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
- Krylov fractality and complexity in generic random matrix ensembles
- Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
- Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
- Krylov space approach to Singular Value Decomposition in non-Hermitian systems
- Spectral statistics of a minimal quantum glass model
- Stable many-body localization under random continuous measurements in the no-click limit
- Anatomy of the eigenstates distribution: a quest for a genuine multifractality
- Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
- The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
- Long-range spectral statistics of the Rosenzweig-Porter model
- Emergent multifractality in power-law decaying eigenstates
- Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
- Spectral form factor and energy correlations in banded random matrices
- Robust extended states in Anderson model on partially disordered random regular graphs
- Localization of Lindbladian Fermions
- Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
- Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
- Anomalous energy correlations and spectral form factor in the nonergodic phase of the -ensemble
- Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
- Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
- Solvable random matrix ensemble with a logarithmic weakly confining potential
- Replica approach to the generalized Rosenzweig-Porter model
- Localization and fractality in disordered Russian Doll model
- Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder