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.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Kondo, Progr. Theor. Phys. 32, 37 (1964)
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975)
Y. Nagaoka, Phys. Rev. A 138, 1112 (1965)
H. Suhl, Phys. Rev. A 138, 515 (1965)
V. Dobrosavljević, T.R. Kirkpatrick, B.G. Kotliar, Phys. Rev. Lett. 69, 1113 (1992)
P.S. Cornaglia, D.R. Grempel, C.A. Balseiro, Phys. Rev. Lett. 96, 117209 (2006)
S. Kettemann, E.R. Mucciolo, J. Exp. Theor. Phys. Lett. 83, 240 (2006)
S. Kettemann, E.R. Mucciolo, I. Varga, K. Slevin, Phys. Rev. B 85, 115112 (2012)
H.Y. Lee, S. Kettemann, Phys. Rev. B 89, 165109 (2014)
B. Shapiro, Philos. Mag. B 56, 1031 (1987)
K. Slevin, P. Markoš, T. Ohtsuki, Phys. Rev. Lett. 86, 3594 (2001)
M.V. Feigel’man, L.B. Ioffe, V.E. Kravtsov, E.A. Yuzbashyan, Phys. Rev. Lett. 98, 027001 (2007)
I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin, Phys. Rev. Lett. 108, 017002 (2012)
F. Evers, A.D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008)
A. Rodriguez, L.J. Vasquez, R.A. Römer, Phys. Rev. B 78, 195107 (2008)
L.J. Vasquez, A. Rodriguez, R.A. Römer, Phys. Rev. B 78, 195106 (2008)
A. Rodriguez, L.J. Vasquez, R.A. Römer, Phys. Rev. Lett. 102, 106406 (2009)
A. Rodriguez, L.J. Vasquez, K. Slevin, R.A. Römer, Phys. Rev. B 84, 134209 (2011)
L. Ujfalusi, I. Varga, Phys. Rev. B 91, 184206 (2015)
E. Cuevas, V.E. Kravtsov, Phys. Rev. B 76, 235119 (2007)
S. Kettemann, E.R. Mucciolo, I. Varga, Phys. Rev. Lett. 103, 126401 (2009)
P.W. Anderson, Phys. Rev. 109, 1492 (1958)
K. Slevin, T. Ohtsuki, New J. Phys. 16, 015012 (2014)
K. Slevin, T. Ohtsuki, J. Phys. Soc. Jpn. 87, 094703 (2018)
A. Weisse, G. Wellein, A. Alvermann, H. Fehske, Rev. Mod. Phys. 78, 275 (2006)
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling,Numerical recipes: the art of scientific computing, 3rd edn. (Cambridge University Press, Cambridge, UK/New York, 2007)
A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Recent Advances in the Theory of Disordered Systems”, edited by Ferenc Iglói and Heiko Rieger.
Rights and permissions
About this article
Cite this article
Slevin, K., Kettemann, S. & Ohtsuki, T. Multifractality and the distribution of the Kondo temperature at the Anderson transition. Eur. Phys. J. B 92, 281 (2019). https://doi.org/10.1140/epjb/e2019-100478-1
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2019-100478-1