The Liouville Theory as a Model for Prelocalized States in Disordered Conductors

Details The Liouville Theory as a Model for Prelocalized States in Disordered Conductors The Liouville Theory as a Model for Prelocalized States in Disordered Conductors

1996-02-29

arxiv.org/abs/cond-mat/9602163v2

Phys.Rev.Lett. 77 (1996) 707

Physics

Condensed Matter

12 pages,revised version,to be published in Phys.Rev.Letters

Scientific paper

10.1103/PhysRevLett.77.707

It is established that the distribution of the zero energy eigenfunctions of (2 + 1)-dimensional Dirac electrons in a random gauge potential is described by the Liouville model. This model has a line of critical points parameterized by the strength of disorder and the scaling dimensions of the inverse participation ratios coincide with the dimensions obtained in the conventional localization theory. From this fact we conclude that the renormalization group trajectory of the latter theory lies in the vicinity of the line of critical points of the Liouville model.

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