Diffusion in the Anderson model in higher dimensions

Abstract

We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites of hypercubic lattices in $d=3-7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behavour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.

References in corpus (12)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• The Kernel Polynomial Method
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Critical properties of the Anderson localization transition and the high dimensional limit
• Dimensional dependence of the metal-insulator transition
• Finite temperature transport in disordered Heisenberg chains
• Universal dynamics of density correlations at the transition to many-body localized state

Cited by in corpus (8)

• Many-Body Localization in the Age of Classical Computing
• Detecting delocalization-localization transitions from full density distributions
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Scale-invariant critical dynamics at eigenstate transitions
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• Critical quantum dynamics of observables at eigenstate transitions
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models