Dyson-Maleev representation of nonlinear sigma-models

TL;DR

The paper demonstrates that the Dyson-Maleev parameterization, originally used for spin systems, can be applied to nonlinear sigma-models across various symmetry classes, simplifying calculations in both perturbative and non-perturbative methods.

Contribution

It extends the Dyson-Maleev parameterization to a broad range of nonlinear sigma-models, providing a new tool for simplifying complex calculations in theoretical physics.

Findings

Applicable to sigma-models in unitary symmetry class

Simplifies diagrammatic and algebraic calculations

Extends to symmetry classes C and B/D

Abstract

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.