2004/12/01 by V. N. Kuzovkov, W. von Niessen
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1140/epjb/e2005-00011-1
published as Eur. Phys. J. B, 42, 529-542 (2004) · 17 pages, 5 figures, to appear in Eur. Phys.J.B
openalex publication_date 2004/12/01 · arxiv created 2005/01/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter \bf 14 (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, <ψ2n,m>, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions D > 2 one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes: low-dimensional systems (2≤ D ≤ 3), where localized states are always exponentially localized and high-dimensional systems (D≥ Dc=4), where states with non-exponential localization are also formed. The value of the upper critical dimension is found to be D0=6 for the Anderson localization problem; this value is also characteristic of a related problem - percolation.