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Symmetry classes of disordered fermions
P. Heinzner, A. Huckleberry, M. R. Zirnbauer
Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their uni…
Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions
T. Spencer, M. R. Zirnbauer
Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H^2, t…
Symmetry classes in random matrix theory
Martin R. Zirnbauer
Dyson's (1962) classification of matrix ensembles is reviewed from a modern perspective, and its recent extension to disordered fermion problems is motivated and described. It is e…
The supersymmetry method of random matrix theory
Martin R. Zirnbauer
The supersymmetry method pioneered by Wegner and Efetov (1979-1983) is reviewed for the case of Hermitian band random matrices, with special attention given to the original method…
Localization from sigma-model geodesics
A. Lamacraft, B. D. Simons, M. R. Zirnbauer
We use a novel method based on the semi-classical analysis of sigma-models to describe the phenomenon of strong localization in quasi one-dimensional conductors, obtaining the full…