Renormalization approach for the two-dimensional Anderson model at the band edge: Scaling of the localization volume

2003/07/31 by Stefanie Russ
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.70.174201

arxiv created 2004/03/15 · openalex publication_date 2004/11/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the localization volumes V (participation ratio) of electronic wave functions in the 2d-Anderson model with diagonal disorder. Using a renormalization procedure, we show that at the band edges, i.e., for energies E\ensuremath≈\ifmmode±\else\textpm\fi4, V is inversely proportional to the variance ⟨ϵ²⟩ of the site potentials. Using scaling arguments, we show that in the neighborhood of E=\ifmmode±\else\textpm\fi4, V scales as V=⟨ϵ²⟩^\ensuremath-1g((4\ensuremath-\ensuremath|E\ensuremath|)∕⟨ϵ²⟩) with the scaling function g(x). Numerical simulations confirm this scaling ansatz.

Citations

• Crossover of level statistics between strong and weak localization in two dimensions
• Electrons in disordered systems and the theory of localization