Renormalization group transformation by moving-bond approach

1977 ◽  
Vol 20 (12) ◽  
pp. 431-434
Author(s):  
E. R. Caianiello ◽  
M. Fusco-Girard ◽  
M. Marinaro
Keyword(s):  
Renormalization Group ◽  
Group Transformation ◽  
Renormalization Group Transformation

scholarly journals A proposal of a Monte Carlo renormalization group transformation

1995 ◽  
Vol 42 (1-3) ◽  
pp. 802-804
Author(s):  
L.A. Fernández ◽  
A. Muñoz Sudupe ◽  
J.J. Ruiz-Lorenzo ◽  
A. Tarancón
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Group Transformation ◽  
Renormalization Group Transformation ◽  
Monte Carlo Renormalization Group

Critical properties of electron eigenstates in incommensurate systems

1984 ◽  
Vol 391 (1801) ◽  
pp. 305-350 ◽  
Keyword(s):  
Renormalization Group ◽  
Critical Point ◽  
Irrational Number ◽  
Localization Length ◽  
Localized States ◽  
Eigenvalue Equation ◽  
Solid State Physics ◽  
Localization Transition ◽  
Group Transformation ◽  
Renormalization Group Transformation

This paper describes some properties of the eigenvalue equation ψ n +1 + ψ n -1 + 2α cos (2πβ n + ∆) ψ n = Eψ n . This is an example of the more general problem of a Hermitian eigenvalue equation in the form of a difference equation with periodic coefficients.These equations arise in solid state physics; they occur in connection with tight-binding models for electrons in one-dimensional solids with an incommensurate modulation of the structure, and in models for the energy bands of Bloch electrons moving in a plane with a perpendicular magnetic field. The model studied has a critical point when α = 1. Following some earlier work by Azbel (Azbel, M. Ya., Phys . Rev . Lett . 43, 1954 (1979)), an approximate renormalization group transformation is derived. This predicts that the spectrum and eigenstates have a remarkable recursive structure at the critical point, which is dependent on the expansion of β as a continued fraction. Also, when β is an irrational number, there is a localization transition from extended states to localized states as α increases through the critical point. This localization transition, which was previously discovered by Aubry & André (Aubry, S. & André, G. Ann. Israel phys . Soc . 3, 133 (1979)) using the Thouless formula for the localization length, is explained by the renormalization group transformation derived here.

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