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Critical Hamiltonians with long range hopping
Author(s) -
Levitov L.S.
Publication year - 1999
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199911)8:7/9<697::aid-andp697>3.0.co;2-w
Subject(s) - physics , exponent , scaling , critical exponent , singularity , distribution (mathematics) , range (aeronautics) , mathematical physics , power law , density of states , statistical physics , quantum mechanics , mathematics , mathematical analysis , phase transition , statistics , philosophy , linguistics , geometry , materials science , composite material
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 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.