Supersymmetric Virial Expansion for Time-Reversal Invariant Disordered Systems

Abstract

We develop a supersymmetric virial expansion for two point correlation functions of almost diagonal Gaussian Random Matrix Ensembles (ADRMT) of the orthogonal symmetry. These ensembles have multiple applications in physics and can be used to study universal properties of time-reversal invariant disordered systems which are either insulators or close to the Anderson localization transition. We derive a two-level contribution to the correlation functions of the generic ADRMT and apply these results to the critical (multifractal) power law banded ADRMT. Analytical results are compared with numerical ones.

13 pages, 1 figure

References in corpus (5)

• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Two-eigenfunction correlation in a multifractal metal and insulator
• Supersymmetry Approach to Almost Diagonal Random Matrices

Cited by in corpus (16)

• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Return probability and scaling exponents in the critical random matrix ensemble
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
• A critical Dyson hierarchical model for the Anderson localization transition
• Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Localization, fractality, and ergodicity in a monitored qubit
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates