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Chebyshev expansion approach to the AC conductivity of the Anderson model

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Abstract.

We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical conductivity \(\sigma(\omega)\) of non-interacting electrons in a random potential (Anderson model) on large three-dimensional clusters. For low frequency the data follows the analytically expected power-law behaviour with an exponent that depends on disorder and has its minimum near the metal-insulator transition, where also the extrapolated DC conductivity continuously goes to zero. In view of the general applicability of the Chebyshev approach we briefly discuss its formulation for interacting quantum systems.

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Authors and Affiliations

  1. School of Physics, The University of New South Wales, NSW 2052, Sydney, Australia

    A. Weisse

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  1. A. Weisse
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Correspondence to A. Weisse.

Additional information

Received: 6 June 2004, Published online: 12 August 2004

PACS:

78.20.Bh Theory, models, and numerical simulation - 72.15.Rn Localisation effects (Anderson or weak localisation) - 05.60.Gg Quantum transport

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Weisse, A. Chebyshev expansion approach to the AC conductivity of the Anderson model. Eur. Phys. J. B 40, 125–128 (2004). https://doi.org/10.1140/epjb/e2004-00250-6

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  • DOI: https://doi.org/10.1140/epjb/e2004-00250-6

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