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Anderson Localization for a Supersymmetric Sigma Model

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Abstract

We study a lattice sigma model which is expected to reflect the Anderson localization and delocalization transition for real symmetric band matrices in 3D. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. The existence of a diffusive phase in 3 dimensions was proved in Disertori et al. (Commun. Math. Phys., doi:10.1007/s00220-010-1117-5, 2009) [2] for low temperatures. Here we prove localization at high temperatures for any dimension d ≥ 1. Our analysis uses Ward identities coming from internal supersymmetry.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Université de Rouen, 76801, St. Etienne du Rouvray, France

    M. Disertori

  2. Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA

    T. Spencer

Authors
  1. M. Disertori
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  2. T. Spencer
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Correspondence to T. Spencer.

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Communicated by M. Salmhofer

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Disertori, M., Spencer, T. Anderson Localization for a Supersymmetric Sigma Model. Commun. Math. Phys. 300, 659–671 (2010). https://doi.org/10.1007/s00220-010-1124-6

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  • DOI: https://doi.org/10.1007/s00220-010-1124-6

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