On the critical level-curvature distribution

Abstract

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form $\bar{P}(K)\sim |K{|}^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.

4 pages, 3 figures

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Cited by in corpus (4)

• Energy level dynamics across the many-body localization transition
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions
• Level dynamics and avoided level crossings in driven disordered quantum dots