Generalized Random-Phase Approximation Theory of Quasiparticle Spectral Functions: Application to Bilayer Quantum Hall Ferromagnets

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We present a microscopic theory of ground-state spectral function of bilayer quantum Hall systems that includes interactions between Hartree-Fock quasiparticles and quantum fluctuations of the order parameter field. The collective modes in these systems are properly described only when fluctuations in direct and exchange particle-hole channels are taken into account. Using an auxiliary field functional integral approach, we present a generalization of the random phase approximation for quasiparticle self-energy which captures fluctuations in both channels. We discuss its relationship to diagrammatic perturbation theory and an adiabatic approximation. We present simple analytical results for the quasiparticle self-energy and the renormalized order parameter that follow from this theory.