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Nonlinear Sigma Model for Normal and Superconducting Systems: A Pedestrian Approach

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arxiv cond-mat/0307471 v1 pith:IMNL2L7H submitted 2003-07-18 cond-mat.mes-hall cond-mat.supr-con

Igor V. Lerner (University of Birmingham , UK) This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.supr-con
keywords approachelectronslecturesmodelnlsmnonlinearpartsigma
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The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what is that, even less so of why it should be used and next to nothing of how it can be applied. These what, why and mainly how are the subject of the present lectures. In the first part, after a short description of why to be bothered, the NLSM is derived from scratch in a relatively simple (but still rather mathematical) way for non-interacting electrons in the presence of disorder, and some illustration of its perturbative usage is given. In the second part it is generalised, not without some leap of faith, to include the Coulomb repulsion and superconducting pairing.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Radiant Field Theory: A Transport Approach to Shaped Wave Transmission through Disordered Media

    math-ph 2024-11 conditional novelty 8.0 of 10

    A new radiant field theory derives the transmission eigenvalue distribution for waves through disordered waveguides beyond the diffusive regime.

  2. Transmission eigenvalue distribution in disordered media from radiant field theory

    math-ph 2024-11 conditional novelty 8.0 of 10

    A matrix transport equation derived from replicated field theory yields the full transmission eigenvalue distribution in disordered media, from quasiballistic to diffusive regimes, for waveguides and infinite slabs.

  3. Non-linear Sigma Model for the Surface Code with Coherent Errors

    cond-mat.stat-mech 2026-03 unverdicted novelty 7.0 of 10

    A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.

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