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Long Range Spatial Correlations in One-Dimensional Anderson Models

Long Range Spatial Correlations in One-Dimensional Anderson Models. Greg M. Petersen Nancy Sandler Ohio University Department of Physics and Astronomy. 1D Anderson Transition?. Evidence For. Evidence Against. Dunlap, Wu, and Phillips, PRL (1990). Abrahams et al. PRL (1979).

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Long Range Spatial Correlations in One-Dimensional Anderson Models

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  1. Long Range Spatial Correlations in One-Dimensional Anderson Models Greg M. Petersen Nancy Sandler Ohio University Department of Physics and Astronomy

  2. 1D Anderson Transition? Evidence For Evidence Against Dunlap, Wu, and Phillips, PRL (1990) Abrahams et al. PRL (1979) Johnston and Kramer Z Phys. B (1986) Kotani and Simon, Commun. Math. Phys (1987) García-García and Cuevas, PRB (2009) Cain et al. EPL (2011) Moura and Lyra, PRL (1998) E/t Greg M. Petersen

  3. The Model α=.1 α=.5 Generation Method: 1. Find spectral density 2. Generate {V(k)} from Gaussian with variance S(k) 3. Apply conditions V(k) = V*(-k) 4. Take inverse FT to get {Єi} α=1 Greg M. Petersen

  4. Recursive Green's Function Method Lead Conductor Lead Also get DOS Klimeck http://nanohub.org/resources/165 (2004) Greg M. Petersen

  5. Verification of Single Parameter Scaling Slope All Localized Greg M. Petersen

  6. Transfer Matrix Method Less Localized More Localized Crossover Energy Greg M. Petersen

  7. Analysis of the Crossing Energy More Localized Less Localized Greg M. Petersen

  8. Participation Ratio - Wavefunctions are characterized by fractal exponents. Greg M. Petersen

  9. Fractal Exponent D of IPR E=0.1 E=2.5 Character of eigenstates changes for alpha less than 1. E=1.3 Greg M. Petersen

  10. Exam Cain et al. EPL (2011) – no transition Petersen, Sandler (2012) - no transition Moura and Lyra, PRL (1998) - transition Greg M. Petersen

  11. Conclusions - Single parameter scaling is verified - All states localize - Found more and less localized regions - Determined dependence of W/t on crossing energy - Calculated the fractal dimension D by IPR - D is conditional dependent on alpha Thank you for your attention! Greg M. Petersen

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