1. O(N) algorithms for disordered systems.
- Author
-
Sacksteder, V. E.
- Subjects
ALGORITHMS ,ALGEBRA ,MATRICES (Mathematics) ,HAMILTONIAN systems ,DIFFERENTIABLE dynamical systems - Abstract
The past 13 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 behaviour across a range of disorders. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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