Perturbation approach to multifractal dimensions for certain critical random matrix ensembles

Abstract

Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models such a direct approach requires modifications which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.

28 pages, 7 figures

References in corpus (3)

• Anderson Transitions
• Exact relations between multifractal exponents at the Anderson transition
• Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

Cited by in corpus (30)

• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• High values of disorder-generated multifractals and logarithmically correlated processes
• Two scenarios for quantum multifractality breakdown
• Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal $1/f$ noise
• Integrable random matrix ensembles
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum
• Multifractal dimensions for critical random matrix ensembles
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Multifractality of quantum wave packets
• Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
• Spectral statistics of Toeplitz matrices
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Statistical properties of structured random matrices
• Multifractality of open quantum systems
• Multifractality of quantum wave functions in the presence of perturbations
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion
• On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes
• Coherent Forward Scattering Peak and Multifractality
• Coherent forward scattering as a robust probe of multifractality in critical disordered media
• Critical dynamics of long-range quantum disordered systems
• Quantum logarithmic multifractality
• Multifractal eigenfunctions for a singular quantum billiard
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Localization and fractality in disordered Russian Doll model
• Virial expansion of the non-linear sigma model in the strong coupling limit