Dyson-Maleev representation of nonlinear sigma-models

Details Dyson-Maleev representation of nonlinear sigma-models Dyson-Maleev representation of nonlinear sigma-models

2008-01-14

arxiv.org/abs/0801.2180v1

J.Phys.A41:215003,2008

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

16 pages, 1 figure

Scientific paper

10.1088/1751-8113/41/21/215003

For nonlinear sigma-models in the unitary symmetry class, the non-linear target space can be parameterized with cubic polynomials. This choice of coordinates has been known previously as the Dyson-Maleev parameterization for spin systems, and we show that it can be applied to a wide range of sigma-models. The practical use of this parameterization includes simplification of diagrammatic calculations (in perturbative methods) and of algebraic manipulations (in non-perturbative approaches). We illustrate the use and specific issues of the Dyson-Maleev parameterization with three examples: the Keldysh sigma-model for time-dependent random Hamiltonians, the supersymmetric sigma-model for random matrices, and the supersymmetric transfer-matrix technique for quasi-one-dimensional disordered wires. We demonstrate that nonlinear sigma-models of unitary-like symmetry classes C and B/D also admit the Dyson-Maleev parameterization.

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