Berlin 2012 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 45: Correlated Electrons: Poster Session
TT 45.46: Poster
Thursday, March 29, 2012, 15:00–19:00, Poster B
A numerical and an analytical approach to Chalker Coddington type network models — •Win Nuding1, Michael Brockmann1, Andreas Klümper1, and Ara Sedrakyan2 — 1Bergische Universität Wuppertal, 42097 Wuppertal, Germany — 2Yerevan Physics Institute, Theoretical Department, Yerevan 36, Armenia
Chalker Coddington type network models appear in the context of the Quantum Hall Effect and the Spin Quantum Hall Effect. These network models and corresponding quantum spin chains are investigated to explain plateau - plateau transitions. In the case of integrable sl(2,1) invariant 3⊗3… spin chains, Bethe Ansatz equations were formulated and solved numerically for small systems. For large systems such numerical calculations are not possible. Therefore an alternative approach on the basis of non linear integral equations (NLIE) is presented. The NLIE can be solved for very large systems giving the scaling dimension.
In the non integrable case row transfer matrices can be calculated explicitly yielding for example Lyapunov exponents and the decay length. Since recent high precision numerical simulations of the Lyapunov exponent in the Chalker-Coddington model [1,2] show disagreement with experimental data, we started numerical simulations of the localization length on random networks.
K. Slevin and T. Ohtsuki, Phys. Rev. B 80, 041304(R) (2009)
M. Amado, A. Malyshev, A. Sedrakyan, F.Dominguez-Adame, Phys.Rev.Lett. 107,066402 (2011)