Quantum logarithmic multifractality
arXiv:2312.17481 · doi:10.1103/PhysRevResearch.6.L032024
Abstract
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing the Anderson transition. In marked contrast to conventional multifractal critical properties observed at finite-dimensional Anderson transitions or scale-invariant second-order phase transitions, in the presence of logarithmic multifractality, eigenstate statistics, spatial correlations, and wave packet dynamics can all exhibit scaling laws which are algebraic in the logarithm of system size or time. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition, such as the many-body localization transition.
10 pages, 5 figures
References in corpus (23)
- Anderson Transitions
- Ergodicity Breaking Transition in Finite Disordered Spin Chains
- Can we study the many-body localisation transition?
- Exact relations between multifractal exponents at the Anderson transition
- Non-ergodic phases in strongly disordered random regular graphs
- Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
- Delocalized Glassy Dynamics and Many Body Localization
- Is there slow particle transport in the MBL phase?
- Multifractal analysis with the probability density function at the three-dimensional Anderson transition
- Critical behavior at the localization transition on random regular graphs
- Dynamical phases in a "multifractal" Rosenzweig-Porter model
- Critical properties of the Anderson localization transition and the high dimensional limit
- Multifractality of wave functions on a Cayley tree: From root to leaves
- The Lévy-Rosenzweig-Porter random matrix ensemble
- Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
- Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
- Return probability and scaling exponents in the critical random matrix ensemble
- Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
- Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
- Random Cantor sets and mini-bands in local spectrum of quantum systems
- Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
- Coherent forward scattering as a robust probe of multifractality in critical disordered media
- Critical dynamics of long-range quantum disordered systems