Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase

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.

11 pages, 6 figures, 89 references

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Cited by in corpus (26)

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• 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 $\beta$-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