Real-space renormalisation-group theory for Anderson localisation: decimation method for electron systems
- 30 June 1980
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 13 (18), 3369-3386
- https://doi.org/10.1088/0022-3719/13/18/006
Abstract
A new real-space renormalisation-group method is developed for electron systems. The equation for the Green function is reduced to that for the Green function in a decimated space to obtain the renormalised Hamiltonian. This formalism is applied to the two-dimensional disordered electron systems in the Anderson model. It is shown that the whole probability distribution Pv(Vij(n); mod ri-rj mod ), of the renormalised transfer energies, Vij(n), can be characterised by gaussian distributions in the logarithmic scale. In particular the average of Vij(n) behaves as (Vjj(n))2)1/2 varies as exp(- gamma (n)(E) mod ri-rj mod ), where the decay coefficient gamma (n)(E) tends to zero as the author approaches the extended regime. The transformation property of the system against decimation is discussed in terms of the flow diagram of the probability distribution functions for the renormalised Hamiltonian.Keywords
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