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We study the ground state properties of the two-dimensional spin-1/2J_1-J_2-Heisenberg model on a square lattice, within diagrammaticapproximations using an auxiliary fermion formulation with exact projection. Ina first approximation we assume a phenomenological width of the pseudofermionspectral function to calculate the magnetization, susceptibilities and the spincorrelation length within RPA, demonstrating the appearance of a paramagneticphase between the Neel ordered and Collinear ordered phases, at sufficientlylarge pseudo fermion damping. Secondly we use a Functional RenormalizationGroup formulation. We find that the conventional truncation scheme omittingthree-particle and higher order vertices is not sufficient. We thereforeinclude self-energy renormalizations in the single-scale propagator as recentlyproposed by Katanin, to preserve Ward identities in a better way. We find Neelorder at g = J_2/J_1 < 0.4 ... 0.45 and Collinear order at g > 0.66 ... 0.68,which is in good agreement with results obtained by numerical studies. In theintervening quantum paramagnetic phase we find enhanced columnar dimer andplaquette fluctuations of equal strength.

J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group