One-Parameter Superscaling at the Metal-Insulator Transition in Three Dimensions

1997/10/31 by Imre Varga, E. Hofstetter, Etienne Hofstetter +2 · 1 citation
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn

paper · pdf · doi:10.1103/physrevlett.82.4683

published as Phys. Rev. Lett 82, 4683 (1999) · 4 pages in PS including 3 figures

arxiv created 1999/04/20 · openalex publication_date 1999/06/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Based on the spectral statistics obtained in numerical simulations on three-dimensional disordered systems within the tight-binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the orthogonal, unitary, and symplectic symmetries ( \ensuremathβ\phantom\rule0ex0ex=\phantom\rule0ex0ex1,2,4) onto a single scaling curve. This relation provides strong evidence for one-parameter scaling existing in these systems which exhibit a second order phase transition. As a result a possible one-parameter family of spacing distribution functions, P_g(s), is given for each symmetry class \ensuremathβ, where g is the dimensionless conductance.

Citations

• Random Matrix Theories in Quantum Physics: Common Concepts
• Statistical electron densities
• The Anderson Transition: Time Reversal Symmetry and Universality

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