Regular Article

Multifractality and the distribution of the Kondo temperature at the Anderson transition^★

¹ Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
² Department of Physics and Earth Sciences, School of Engineering and Science, Jacobs University Bremen, Bremen 28759, Germany
³ Physics Division, Sophia University, Chiyoda, Tokyo 102-8554, Japan

^a e-mail: slevin@phys.sci.osaka-u.ac.jp

Received: 2 October 2019
Published online: 25 December 2019

Abstract

Using numerical simulations, we investigate the distribution of Kondo temperatures at the Anderson transition. In agreement with previous work, we find that the distribution has a long tail at small Kondo temperatures. Recently, an approximation for the tail of the distribution was derived analytically. This approximation takes into account the multifractal distribution of the wavefunction amplitudes (in the parabolic approximation), and power law correlations between wave function intensities, at the Anderson transition. It was predicted that the distribution of Kondo temperatures has a power law tail with a universal exponent. Here, we attempt to check that this prediction holds in a numerical simulation of Anderson’s model of localisation in three dimensions.