O(N) algorithms for disordered systems

Vincent E. Sacksteder

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arXiv · cond-mat/0312046

O(N) algorithms for disordered systems

Vincent E. Sacksteder

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Abstract

The past thirteen years have seen the development of many algorithms for approximating matrix functions in O(N) time, where N is the basis size. These O(N) algorithms rely on assumptions about the spatial locality of the matrix function; therefore their validity depends very much on the argument of the matrix function. In this article I carefully examine the validity of certain O(N) algorithms when applied to hamiltonians of disordered systems. I focus on the prototypical disordered system, the Anderson model. I find that O(N) algorithms for the density matrix function can be used well below the Anderson transition (i.e. in the metallic phase;) they fail only when the coherence length becomes large. This paper also includes some experimental results about the Anderson model's behavior across a range of disorders.

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BibTeX RIS

Vincent E. Sacksteder. 2004-04-30. O(N) algorithms for disordered systems. https://arxiv.org/abs/cond-mat/0312046

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