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Highly efficient numerical implementation of the Chalker-Coddington network model and applications

Highly efficient numerical implementation of the Chalker-Coddington network model and applications

 S. Bera, F. Evers and I. Kondov


In: Computational Methods in Science and Engineering: Proceedings of the Workshop SimLabs@KIT, pp. 47-57, Karlsruhe, KIT Scientific Publishing, 2011.

Datum: 2011

A formulation of quantum dynamics at the Anderson transition in terms of a network model was introduced by Chalker and Coddington in 1988 to describe the integer quantum Hall effect. Such network models have been systematically exploited in both analytical studies and numerical simulations and played a key role in advancing our understanding of quantum Hall critical points, including not only the conventional integer quantum Hall effect but also systems with unconventional symmetries. On the other hand, highly efficient numerical routines for diagonalizing sparse matrices that have been developed over the last decade. Combined with the increase in computer power and an improved understanding of finitesize effects, this development has recently paved the way for highly accurate numerical studies of critical behavior for a variety of Anderson critical points.

Recently, we have developed a highly optimized numerical implementation of the Chalker–Coddington network model (CCNM) with intensive use of sparse matrix libraries ARPACK and MUMPS for diagonalization and solving linear equations, respectively. In particular, we have performed detailed profiling of the serial code and subsequently employed multi-layer strategies for parallelization. The dimension of the matrices computed is of the order of 10 million x 10 million and 106 disorder realizations have been done. For the computations the parallel machine HP XC3000 (HC3) at KIT has been used. The favorable scaling of the implementation allowed to investigate the interaction effect at the integer quantum Hall transition (IQHT) as well as relations between point contact conductance and multifractality in the numerical framework using the CCNM.