Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime

Abstract

We construct perturbation series for the q-th moment of eigenfunctions of various critical random matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dimensions Delta(q)=Delta(1-q), recently conjectured for critical models where an analogue of the metal-insulator transition takes place. It is known that this relation is verified at leading order in the weak multifractality regime. Our results thus indicate that this symmetry holds in both limits of small and large coupling constant. For general values of the coupling constant we present careful numerical verifications of this symmetry relation for different critical random matrix ensembles. We also present an example of a system closely related to one of these critical ensembles, but where the symmetry relation, at least numerically, is not fulfilled.

12 pages, 12 figures

References in corpus (11)

• Anderson Transitions
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization of ultrasound in a three-dimensional elastic network
• Exact relations between multifractal exponents at the Anderson transition
• Eigenfunction entropy and spectral compressibility for critical random matrix ensembles
• Symmetries of multifractal spectra and field theories of Anderson localization
• Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
• Multifractal wave functions of simple quantum maps
• Return probability and scaling exponents in the critical random matrix ensemble
• Integrable random matrix ensembles
• Universal and non-universal features of the multifractality exponents of critical wave-functions

Cited by in corpus (26)

• 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 Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• 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
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• 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
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Spectral statistics of Toeplitz matrices
• Multifractality of open quantum systems
• Multifractality of quantum wave functions in the presence of perturbations
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• 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
• Quantum multifractality as a probe of phase space in the Dicke model
• 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
• Fractal states of the Schwinger model
• Quantum logarithmic multifractality
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Multifractality in the fidelity of the Toffoli gate