J1-J2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group

We study the ground-state properties of the two-dimensional spin-1/2 J(1)-J(2) Heisenberg model on a square lattice, within diagrammatic approximations using an auxiliary-fermion formulation with exact projection. In a first approximation, we assume a phenomenological width of the pseudofermion spectral function to calculate the magnetization, susceptibilities, and the spin-correlation length within random-phase approximation, demonstrating the appearance of a paramagnetic phase between the Neel-ordered and Collinear-ordered phases, at sufficiently large pseudofermion damping. Second we use a functional renormalization-group formulation. We find that the conventional truncation scheme omitting three-particle and higher-order vertices is not sufficient. We therefore include self-energy renormalizations in the single-scale propagator as recently proposed by Katanin, to preserve Ward identities in a better way. We find Neel order at g=J(2)/J(1) less than or similar to g(c1) approximate to 0.4...0.45 and Collinear order at g greater than or similar to g(c2) approximate to 0.66...0.68, which is in good agreement with results obtained by numerical studies. In the intervening quantum paramagnetic phase, we find enhanced columnar dimer and plaquette fluctuations of equal strength.