Critical Hamiltonians with long range hopping

Details Critical Hamiltonians with long range hopping Critical Hamiltonians with long range hopping

1999-08-12

arxiv.org/abs/cond-mat/9908178v2

Ann. Phys. (Berlin) 8 (7-9) 697-706 (1999)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 5 eps figures, LaTeX uses annalen.cls style (included), proceedings of Localization 99

Scientific paper

10.1002/(SICI)1521-3889(199911)8

Critical states are studied by a real space RG in the problem with strong diagonal disorder and long range power law hopping. The RG flow of the distribution of coupling parameters is characterized by a family of non-trivial 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 two-level 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.

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