Localization, Dirac Fermions and Onsager Universality

Details Localization, Dirac Fermions and Onsager Universality Localization, Dirac Fermions and Onsager Universality

2001-11-30

arxiv.org/abs/cond-mat/0111583v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

To appear in EPJ; Proceedings of Internation conference on Geometry and Integrability

Scientific paper

10.1140/epjb/e2002-00314-7

Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universality of the localized fermions where the fluctuations in localized wave functions are universal. We further show that the fluctuations about localized nonrelativistic fermions describe relativistic fermions. This provides a new approach to understand the absence of localization in disordered Dirac fermions. We investigate how disorder affects well known universality of the spin chains by examining the multifractal exponents. Finally, we examine the effects of correlations on the localization characteristics of relativistic fermions.

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