Critical Hamiltonians with long range hopping
Abstract
Critical states are studied by a real space RG in the problem with strong diagonal disorder and long range power law hopping. The RG ow of the distribution of coupling parameters is characterized by a family of nontrivial fix points. We consider the RG flow of the distribution of participation ratios of eigenstates. Scaling of participation ratios is sensitive to the nature of the RG fix point. For some fix points, scaling of participation ratios is characterized by a distribution of exponents, rather than by a single exponent.The RG method can be generalized to treat certain fermionic Hamiltonians with disorder and long range hopping. We derive the RG for a model of interacting twolevel systems. Besides couplings, in this problem the RG includes the density of states. The density of states is renormalized so that it develops a singularity near zero energy.
 Publication:

Annalen der Physik
 Pub Date:
 November 1999
 DOI:
 10.1002/(SICI)15213889(199911)8:7/9<697::AIDANDP697>3.0.CO;2W
 arXiv:
 arXiv:condmat/9908178
 Bibcode:
 1999AnP...511..697L
 Keywords:

 localization; scaling; multifractality;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 10 pages, 5 eps figures, LaTeX uses annalen.cls style (included), proceedings of Localization 99