Dyson-Maleev representation of nonlinear sigma-models

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.

16 pages, 1 figure

References in corpus (16)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Statistics of energy levels and eigenfunctions in disordered systems
• Riemannian symmetric superspaces and their origin in random matrix theory
• Electron--electron Interactions in Disordered Metals: Keldysh Formalism
• Spectral Statistics Beyond Random Matrix Theory
• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• Dynamic localization in quantum dots: analytical theory
• Representation theory of sl(2|1)
• The supersymmetric technique for random-matrix ensembles with zero eigenvalues
• Spin-Wave Theory and Finite-Size Scaling for the Heisenberg Antiferromagnet
• Non-perturbative results for level correlations from the replica nonlinear sigma model
• Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs Anderson localization
• Local correlations of different eigenfunctions in a disordered wire
• Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime
• Quantum mechanics with a time-dependent random unitary Hamiltonian: A perturbative study of the nonlinear Keldysh sigma-model
• Quantum correction to the Kubo formula in closed mesoscopic systems

Cited by in corpus (3)

• Correlations of the local density of states in quasi-one-dimensional wires
• Superconducting proximity effect in quantum wires without time-reversal symmetry
• Anderson localization of a Majorana fermion